What can I seal a porous bird bath with?

You can coat it with epoxy!

http://homeguides.sfgate.com/seal-concrete-birdbath-52526.html

Get FlexSeal. Its a spray on rubber coating that they say is non-toxic once dry. It can be used on fish ponds as well.

I have the same issue with my birdbath, and plan to do this. It's been a really wet spring for us here, so I haven't done it yet. I'm hoping that this will provide protection in the winter too, so the moisture doesn't cause any cracking with the freeze-thaw cycle. (I got mine at Lowes, but I think I've seen it at Walmart too)

flex seal is also great in showers the master bath had to have tiles repainted and we sealed with the flex seal worked great non slippy surface and no more flaking of color

I would line it with a planter saucer. Guaranteed not to leak!

Also, you can lift it out to wash it when you need to. (I would use a light weight plastic one instead of a terra cotta liner)