Becky was a dance teacher. She was one of the few people to know the Doctor's real name. She was also married to David.
When Becky was a teenager, she met the Sixth Doctor. He pretended that she had won a contest to learn how to dance. He taught her the waltz and the foxtrot. He also tried to convince her that she should follow her dream of being a ballet dancer. However, she was more interested in practising "snogging" with her friend David, whom she said was not her boyfriend.
Becky met the Doctor again when she was middle-aged and unhappy in her marriage. She taught him the waltz and the foxtrot and was romantically interested in him. She told him of her childhood dream of being a ballet dancer.
The Doctor next met Becky when she was in her eighties and bed-ridden. He invited her to travel with him, but she refused. (PROSE: Teach Yourself Ballroom Dancing)