I'm sorely lacking in 4th ed knowledge, but here are some basics for you to consider:
1 - EXPOSURE: That bridge is brutally open, making it a natural murder zone if the defending force is prepared with missiles or skirmishers. Reducing line of sight to the bridge is of critical import. Consider using fire from your artillery (clay pots filled with flammables and/or greek fire, will get stuff burning but good) to create a smoke/hazard from a distance (building 3 is a convenient target). That will hopefully create a natural wall of fire/smoke to screen your crossing. Various spell effects will help you get troops across while taking a minimum of casualties.
Good use of your ambushers from the east to create a skirmish/distraction will help pull attention away from your crossing as well.
Anyway you slice it, though, you're going to have to cross under fire and into resistance. Consider pavise-style portable-cover on wheels to screen from the worse of it, or other variants on a battering ram/siege tower to cross the river if they go with missiles.
2 - PUSH OF PIKE: Once the crossing is secured from missile fire, they'll seek to deny you the physical ability to cross. Pike phalanx would be my go-to option with swordsmen mixed up among the front rank to handle anyone who got under the spears. It should go without saying that you're going to want your heaviest vanguard on point for the crossing. Think 'wrecking ball' and you're in good shape - but a slow moving one. The good news for pike formations is that they're bunched up - prime AoE ability fodder.
3 - AREA DENIAL COUNTERMEASURES: Expect them to consider blowing the bridge as a real option, especially if they're out-classed. You'll want counters to obvious spells and abilities that could damage the bridge - ESPECIALLY when your vanguard is crossing it.
4 - AIR SUPPORT: I don't know if Tar Devils can fly but if they can, or if you have any other airborne units, use that. Drop buckets of burning pitch, greek fire, whatever you can to disrupt enemy formations, break down their line of communication/sight, and otherwise foul up their day. Ideally use something you can selectively extinguish, to prevent your own forces from falling into the same trap.
5 - ONCE ACROSS: Feed your own pike wall equivalents and establish an expanding schiltron. You are at your most vulnerable when half of your forces are across, that's when a savvy enemy will hit you, and try to bust the bridge if they haven't already. If they can split your force in half they can apply their full pressure to half your strength and then mop you up. An educated commander will expect this.
6 - ALTERNATE CROSSINGS: Consult spells and magical abilities you may have available which can effect the flow of the river or its depth (make a ford). Consider the forest in the southwest as a source of wood. Log jams could be constructed or similar makeshift crossings secured. A particularly determined/unscrupulous commander could simply go for artillery-fired ropes of sufficient length and order troops to ford the river, using the rope to keep themselves above water. It's slow going and low through-put, and losses will be heavy but See Also: Evil. :P
7 - ARTILLERY SUPPRESSION: Consider parking artillery on the near bank and using it to suppress the far bank. While completely anachronistic, it should be quite effective until they can silence your battery. The idea is to smash stuff and make fire and generally convince defending archery that its better if they just pack it up and go home. :)
YMMV. Have fun!