I think the birds would feel alot safer if there was a large open area around the birdbath with good visibility i.e. no vegetation (maybe just short groundcover plants). The birds don't know the plants are prickly to deter the cat, and they might not use the bath because they can't see predators in the thicket.
I know my birdbath gets used alot more since I moved it out to a more visibly clear area. I have a tree close by for them to skedaddle to if they sense danger.

low growing blueberries?

Barb
southern Ontario, CANADA

It's out in the open now with two trees within 10'. The little fence perimeter is definitely effective. Not a single kill since I put it up. I'll probably just emulate that in the form of plants, leaving a clear area about 3' all the way around the bird bath. My cat would have to be one heck of a gymnast to get over a bed of shrubs, into the clearing and onto the bath to catch one by surprise.

If you put in a "prickly" border how would you get to it to add water and give it a scrubbing?

If you have a source for pine cones, you could fill that 3' area with them. I've read that cats don't like to walk on them.

Or you could suspend chicken wire a couple of inches above the ground (stapled to stakes?) and plant something low-growing that would grow up through the wire, hiding it. You might have to extract the kitty from the whole business...but only once I would think.

pyracantha or barberry would be another good prickly choice

Hi Rudy - good idea to move the birdbath into the open, with trees/shrubs nearby for the birds to preen and escape to cover if necessary. My instincts say the birds prefer the immediate area to be open so they can watch for predators.

I don't generally grow anything under the bird baths, maybe a few low-growing annuals. I mulch underneath them by first laying down cardboard and and then adding a couple inches of aged woods chips, to keep the weeds down.