Complex sentence: In early 1956, after a bidding war between the two subsidiaries of King Records wanting to sign them, one from a Miami executive and another from Atlanta executive Ralph Bass, Bass won them over and signed them to Federal Records.
Split into simpler sentences: In early 1956, they were the subject of a bidding war between two subsidiaries of King Records, one based in Miami and one in Atlanta. The Atlanta executive was Ralph Bass, who won them over and signed them to Federal Records.