I say it like I heard it with the emphasis on the first syllable. A bulene. But I've noticed that Yankees have a tendency to put the stress on the ending. Abuh LEENE.
Similar tendencies affect other local communities. Think about Tuxedo. (TUX uh doh vs. tucks EE duh).Or even Colorado City (Cahl oh ray duh vs. Cahl uh rah doh).
It reminds me of the question about the pronunciation of the capital of Louisiana. Is it Nahluns or New Or LEENS? Actually, the capital of Louisiana is Baton Rouge. But you knew that didn't you?
By the way, according to The Handbook of Texas Online, our Abilene, Texas was named after the Kansas cattle town.