To "give bat" is to firmly resist someone's romantic advances. It use is occasionally also extended to more general cases of being turned down.
It is a South African slang term, that probably first appeared in 1990s. It most likely has its origins in cricket - the metaphor being one of a bowler attempting to bowl a batsman out by bowling at the stumps, only to have to have the batsman play a non-scoring, blocking shot by placing his bat solidly in the balls trajectory.
I tried to kiss her at the party, but she gave me bat.