If you're old enough, watch some of the Showtime series Sparticus. It's not the most realistic combat, but neither is Pathfinder so it evens out. There are a few times in the series that characters use shields to bash opponents away, even when they've been knocked down.
Typically, they are leaning on their hands and knees to get up, so you could say that's why it works but, more generally, if you're a Fighter (or similar) with that much effort put into shield use, you find ways to make what you want work.
Functionally, you can Bull Rush a Prone target because there is no point in the rules that says you can't:
You can make a bull rush as a standard action or as part of a charge, in place of the melee attack. You can only bull rush an opponent who is no more than one size category larger than you. A bull rush attempts to push an opponent straight back without doing any harm. If you do not have the Improved Bull Rush feat, or a similar ability, initiating a bull rush provokes an attack of opportunity from the target of your maneuver.
If your attack is successful, your target is pushed back 5 feet. For every 5 by which your attack exceeds your opponent's CMD you can push the target back an additional 5 feet. You can move with the target if you wish but you must have the available movement to do so. If your attack fails, your movement ends in front of the target.
The character is lying on the ground. A prone attacker has a –4 penalty on melee attack rolls and cannot use a ranged weapon (except for a crossbow). A prone defender gains a +4 bonus to Armor Class against ranged attacks, but takes a –4 penalty to AC against melee attacks.
Standing up is a move-equivalent action that provokes an attack of opportunity.
Nowhere in Prone does it indicate that you can't inflict other conditions or that they can't be moved (or move for that matter, but that's another question).
As to whether Improved Shield Bash works, it does not.
However! Any attack bonus to shields (including their -4 AC from being Prone) does. And that can be just as good if not better. Taking Weapon Focus(type Shield) or investing in a magic shield spike allow you to take a feat that is constantly useful for your build, or spend money to increase your success rate.
Source: From Shield Slam
..substituting your attack roll for the combat maneuver check...
This indicates that the entire CMB check is replaced, not just the die roll. You use your rolled chance to hit instead of any Maneuver bonuses.