I don't think it's Velvet but there are some things that need your attention..
Your tank is heated and it's only 72? Why? Bettas are tropical fish and need a constant unchanging temp somewhere between 78-80F. You should also use an in tank thermometer to monitor temp.
Although a 50% weekly change with siphon (siphon is needed to remove debris from the gravel and just scooping water off the top is not enough) is enough, a new tank will require more frequent water changes and closer monitoring.
Cycling takes up to 2 months and during this time you should be testing daily for ammonia and nitrite and doing an extra 50% change any time either show up. In addition to this a regular 50% weekly change with siphon is needed. First you will see ammonia spike, then you will see nitrites. Eventually, even after a week of no water changes ammonia will stay at 0, then finally nitrites. At this point you should be left with only nitrates, which should be kept <20ppm and the lower the betta by the once weekly change with siphon.
So.. if your pet store will test daily like this and give you actual numbers, I guess you can get away with free tests.
I think if you just pick up monitoring and changes and warm her up slowly she will be okay. It sounds like she has just lost color from being cold and stressed.