I am already in an ADN program and am starting my second term. Is it possible to transfer the credits from the first term into a BSN program and continue from there, or do I just have to finish the ADN program then look into getting a BSN?
It depends on the program. This isn't something that we can answer for you. You would have to investigate the BSN programs that you are interested in applying for.
My guess, based on past experiences, is that your general education requirements will transfer, but the great majority of nursing courses will not. Most programs will require that nursing courses are taken at their university. Some basic classes might transfer (fundamentals, pharmacology) but that will, again, depend on the school you are transferring to.
I'm curious why you want to transfer now. The fall deadline for the great majority of BSN programs is past- so you even if you applied for a BSN program now, you wouldn't be able to start until spring at the earliest. So your second term would be over before you even started the BSN program. Then you would only have a year left in your ADN program, and if you went straight to an RN-BSN program then you could be done in 1.5 years. That's 3 years total from where you are right now.
However, if you transfer into a BSN program now, you'll have, minimum, three more years before you graduate, and possibly more depending on what credits don't transfer. So you'll end up graduating at the same time, with the same degree, no matter which route you choose.