Biking might help your shins, to maintain your general cardiac fitness, you can do bike rides where you maintain 90 rpm's or more and maybe roughly double the duration you would be out for a run. You need to feel like you are pushing yorself a bit on the bike, a heart monitor can help.

For strength, doing repeats up longer hills while seated is excellent

You can do intervals just like on the track, just use the road and do them by time, same for tempo

Shin splints are partially caused by your calf muscles being disproportionately stronger than the muscles on your shins. Cycling might push it further out of wack, since that can involve a lot of calf usage. You might want to add in some shin exercises.

The best one I've come across for alleviating shin splints is to sit in a chair with one foot off the ground and write the alphabet with your foot. Then do the same with the other foot. I might do that a few times a night and the splits are gone in short order.

Cycling is my favorite cross-training activity to help with recovery from running injury while maintaining fitness. Like jroden said, you probably have to double the duration to get the same benefit as running. I don't have access to a pool, but if I did I would certainly substitute that in too.

Hope this helps, and good luck with the recovery.

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-Todd
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There's plenty of time for rest when you're dead.