Meic Stephens in "Welsh Names for your Children: A Complete Guide" Lists Bet, Beti, Bethan, Betsan, Betsi and Bessi all as diminutive forms of Elisabeth.
I believe I read once in "Welsh Surnames" by T.J Morgan and Prys Morgan that the deminutive -an was a common Welsh ending for 'standard' nicknames such as Meg - Megan.