I don't know anything about this product - but it looks like if you wanted to use it in bridged mode, you'd have to make some modifications to the board, plus you'd have to use two boards stacked on top of each other (I guess). You'd have to cut some traces, and wire around others. See figure 7 in the datasheet (page 7). Basically, the enable pins (6 and 11) are wired together for a singular enable. On the shield, these are the PMWA and PMWB pins; so on one each board, you would want to wire both together, but only choose one of the pins to control both (board 1 would be PMWA pin jumpered to the PMWB pin, and the PMWB pin disabled, board 2 would be the PMWB pin jumpered to the PMWA pin, and the PMWB pin disabled). You'd have to do something similar with the IN1 and IN2 pins (jumpered to the IN3 and IN4 pins); the crazy thing here is that a set of the pins are inverted (with a 7404 variant) - you'd have to bypass that as well. Finally, you'd have to jumper together OUT1 and OUT2 with OUT3 and OUT4 (fortunately, since these have nothing to do with the Arduino, and there seems to be a jumper block that could be used for this purpose (?).
The biggest problem I see, though, is that it doesn't seem like the package is properly heatsinked on that shield (and a proper heatsink would likely preclude using it as a shield!). Page 2 seems to indicate that the PowerSO20 package, to use it to its full spec - needs to be mounted in some manner to an aluminum substrate (on the bottom of the chip package, I think) - which would then likely pass the heat output to a heatsink (or the substrate would -be- the heatsink).
In the case of this shield by SparkFun, there isn't a heatsink, just the PCB material. I doubt as it is currently set up - even using the L298 to control two separate motors - you couldn't run each motor up to the full 2A rating; there'd be no place for the chip to dump the heat, and it would burn out (or go into thermal overload mode). You would probably be lucky to get up to 1A for each motor (and it would probably be running hot to the touch then).
I wouldn't try the bridge mode on this shield - it wouldn't be worth it. You'd do better to get the Multiwatt15 and proper heatsinks; the downside is the funky pin spacing, but I've bought some special L298 adapter PCBs, and they work well:http://www.phoenixgarage.org/show_article/123
That, or your could etch your own layout on a PCB (which might be a better option - build your own L298 motor controller card, and run jumpers from the Arduino to it for control).