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