The 6th-level Sor/Wiz spell antimagic field [abjur] (Player's Handbook 200), in part, says, "Should a creature be larger than the area enclosed by the [antimagic] barrier, any part of it that lies outside the barrier is unaffected by the field." The Rules Compendium on Antimagic on Creatures expands this further saying, in part, that
A big creature whose space is partially within an antimagic area can choose to attack from a square not within the area, thereby suffering no adverse effects from the antimagic. Its attacks and abilities are affected by the antimagic if it attacks into the antimagic area or uses an ability on a foe within the antimagic area. (11 and emphasis mine)
(This text doesn't appear in the PH, Monster Manual, or Dungeon Master's Guide—and if it appeared in another text before the RC then this writer doesn't know which text. Thus its provenance may mean this rule doesn't apply in your campaign—see here and ask the DM.) Contrast that RC quotation above with the beginning of the Rules Compendium's next paragraph: "Summoned creatures of any type disappear if they enter an antimagic area. Incorporeal creatures do the same" (11). With these rules in mind, this answer takes what I expect will be a somewhat controversial position. (To be fair, though, I'm not sure there are any noncontroversial positions where antimagic is concerned.)
To summarize both the Rules Compendium and the Dungeon Master's Guide, a magic effect that affects an area is suppressed when its point of origin is in an area of antimagic. Further, a magic effect that affects an area sees its area correspondingly suppressed when that magic area overlaps with an area of antimagic. However, according to the RC, a magic effect that doesn't affect an area and that has as its subject that big creature seems to be unaffected when a big creature is only partially in an area of antimagic.
That's because a creature "can choose to attack from a square not within the area, thereby suffering no adverse effects from the antimagic." Since a big creature that's only partially in an area of antimagic can still use magic normally (except against parts of creatures in the area of antimagic), likewise it should be able to use its own magic against itself while partially in an area of antimagic. (An area of antimagic doesn't block line of effect, and a creature always has line of effect to itself.) Extending this even more, a magic effect present on a creature when it only partially enters an area of antimagic should not be suppressed.
Anyway, to sum up, unless a creature's entire space is enclosed in an area of antimagic, the creature's magic continues to function normally on itself, the creature can use magic normally on itself, and the creature can use magic normally to affect stuff outside the area of antimagic.
"That sounds a little fishy…"
Yeah, I know, and I also know that it may sound incredibly awkward. In practice, though, it seems at least better than the obvious alternatives. For example, this reading neatly answers the question of what happens when a were-giant squid gnome in giant squid form slides just 1 square of itself into an area of antimagic: pretty much nothing.
One alternative to this reading sees a were-giant squid gnome in giant squid form flicker infinitely and unresolvably between the assumed giant squid form and the original gnome form, the assumed form partially occupying the area of antimagic and the original form not. ("So, do we all just go play video games now or what?") Another alternative would have the DM determine which part of the giant squid from assumes original gnome form while the creature is partially in an area of antimagic. Neither alternative is playable. (Although I do credit this fine answer with ingeniously bypassing that first outcome!)
Further, this reading would have what happens to an incorporeal or summoned creature be distinct from what happens to other creatures. That is, a big creature—whether or not it's the subject of form-changing magic—is not wholly affected by an area of antimagic if it's only partially within an area of antimagic: both the DMG and the RC agree on that. Incorporeal creatures and summoned creatures are their own specific cases so those rules don't apply. (Big incorporeal or summoned creatures still wink out, though, because that's specifically what happens when "they enter the area of an antimagic effect" (DMG 290 and emphasis mine).)
Finally, just to be clear, when a creature's space is wholly engulfed by an area of antimagic, a creature's magic form-changing effect is suppressed: it resumes its original form, and it stays in that original form until at least one square of the original form's space is outside the area of antimagic—and if that happens the magic form-changing effect resumes if its duration permits.
"Who picks what squares a creature occupies when the creature's size category changes?"
The DM must answer that question; the game doesn't. (The DM may consider applying generally details from the description of the 1st-level Sor/Wiz spell enlarge person [trans] (PH 226–7), but even then the question's still, like, 98% unanswered.)
Usually, this reader would advocate that the creature who is changing size pick the legal squares it occupies, but that's typically because the creature is changing size voluntarily rather than have its size changed involuntarily. The size changer has no stake in an area of antimagic or another's dispel magic effect—it's just another hapless victim. That said, unless persuasive alternatives were put forth, this DM would likely let the dice decide the squares the creature occupies .
What happens using this reading when an attacker that's protected by an area of antimagic makes a bull rush attempt against a defender that's affected by a magic form-changing effect
If the attacker's area of antimagic does not completely engulf the defender's space, the defender's magic form-changing effect is unaffected and the attacker makes bull rush attempts against the defender while the defender's in the form it assumed using its magic form-changing effect.
If the attacker's area of antimagic completely engulfs the defender's space, the defender's magic form-changing effect is suppressed while the defender's space is engulfed and the attacker makes bull rush attempts against the defender while the defender's in its original form.
If the attacker is charging and the attacker's area of antimagic completely engulfs the defender's space, the defender's magic form-changing effect is suppressed. If the size of the form the defender assumed using its magic form-changing effect is different from the size of the defender's original form, the DM determines the squares the defender's original form occupies. It's possible for the typical attacker's charge to be spoiled by the defender becoming bigger or littler if, for example, the defender's location now requires the attacker to turn to complete the charge.
However, if the attacker is just moving, the suppression of the defender's magic form-changing effect doesn't affect the attacker's movement. The attacker can continue his movement and does so with knowledge of the changed battlefield conditions (e.g. the giant squid is now a gnome). For example, on his turn the attacker can take a move action to move 15 ft. so that his area of antimagic engulfs the defender, a giant squid, suppressing the giant squid's magic form-changing effect and returning it to its original form, a gnome. Then the DM determines where defender's original form appears among the squares once occupied by the assumed form. Afterward, the attacker can continue his move action and head toward that gnome. And, when the attacker's adjacent to that gnome, he can take a standard action to make a bull rush attempt against that pesky gnome.
Finally, if the attacker's successful bull rush moves the defender's space even partially out of the area of antimagic, the defender's magic form-changing effect resumes if its duration allows.
Note: Whether or not a creature that's protected by an antimagic field spell that's been modified by the Complete Arcane metamagic feat Persistent Spell (81) then further enhanced by the Complete Adventurer feat Extraordinary Spell Aim (109) is immune to magic as if the creature were itself actually in that antimagic field is beyond this question's scope. (Also see this question.) Nonetheless, bear in mind that an area of antimagic in D&D 3.5 does not block line of effect like it did prior to the 3.5 revision. Suffice it to say, this seems to work in the campaign you're in, so have fun, and try not to overshadow everyone else.