here is a site that has a huge list of B names along with their meanings, below you can see the page list, and on each of those pages there is at least 5 names listed. Good luck she is a sweetie
http://www.thinkbabynames.com/list/0/B
Babe - Bambi | Baptista - Basilia | Basma - Bebba | Becca - Beige | Béibhinn - Belva | Bena - Berdine | Berengaria - Bertina | Bertrade - Bethany | Bethea - Bevin | Bianca - Bird | Birdena - Blanda | Blasia - Bluebell | Blythe - Bonnie | Borbala - Breck | Breda - Briar | Brice - Briony | Brisa - Bronwyn | Brooke - Buena | Buffy - Burnett