Just curious, is there a way to block someone from trying to book you?

You should say "I'm sorry I won't be able to care for your dog. Here is Rover match number and they can assist with alternate aitters".

If you say Im not available you're avoiding the issue and then they wonder whats going on: did she not see the dates, did someone cancel, is she open now etc etc. Saying no will produce the result you want. Right now, they don't know you're creeped out and they think they're a normal person. You don't have to give reason why no. Just state it and they'll go elsewhere. If they don't then contact rover support.