There are no words that start with B and rhyme with abrasive.
One word that rhymes with "cup" and starts with "B" is "blup."
bule
Butt, buzzcut
resilient
bundamentalls
ball
break
brook
A word that rhymes with blue and starts with B is "blew," which is the past tense of the verb "blow."
persuasive
Bostitch Blair Witch
Bead, bleed, breed.