Bamber rhymes with:
amber, amber's, camber, cambre, clamber, gamber, kamber, schamber, amber, amber's, bedchamber, camber, cambre, chamber, clamber, cucumber, cumber, december, dismember, ember, encumber, gamber, humber, imber, kamber, kimber, limber, lumber, macomber, macumber, mccomber, mccumber, mcomber, member, misremember, nonmember, nov, november, number, outnumber, pember, remember, schamber, sember, september, slumber, somber, timber, timbre, unencumber
Bamber sounds like:
banbury, bembry, benfer, bomber, bonfire, bumper