Bridgette to Betsy?

[thellamaqueen.livejournal.com]

I posted yesterday looking for first names that worked with the middle name Betsy.
My husband and I talked about it some more, and started looking for more first names that could be shortened to use Betsy as a nickname... and we stumbled across a name we both liked:  Bridgette.
Would it be feasible to say that Betsy could be a nickname for Bridgette? 
I was to the point of finding any female name with a B, an E and a T in it and shortening it to Betsy when we found this name... but I think it works... WDYT?
Also: our last name is Beedon.  Is "Betsy Beedon" too cutesy sounding?  I'm growing accustomed to the sound of Bridgette Beedon... but Betsy Beedon, I'm not so sure of. 
One of our Aunt Betsys also has a last name that starts with a B (a different name from ours), and I think it sounds very cute together, but the cuteness fits her well.