Safety

BASE jumping is inherently dangerous, and you can be seriously injured or killed on any jump. Training and preparation help reduce the risk, but even the most experienced jumpers get killed. Bridge Day provides a good environment for your first BASE jump because:

Altitude. You have a lot more time to recover from a bad exit than at the Perrine. (half the height).
Landing. You can take the water and highly experienced rescue personnel will have you out of the water, usually in seconds.
Experienced help. Bridge Day is all about the first time jumper, and every year, experienced staff check each jumper's gear prior to exiting the bridge. Every year, issues are caught that could have caused a fatality.
Training. First time jumpers with their Bridge Day training course. Register

What can you do to avoid a ride in one of these?

Landing in the water is pretty much the only sure fire method to stay safe, but practicing your canopy skills is a strong second. Pack your intended BASE canopy into a skydiving rig and make as many jumps as you can. Try to hit dead center in the peas, and try it cross wind and down wind, because you may have to do land that way in the gorge.