Are we ever told? And, how does Betty stay at the local JC if she is a senior?

I think Bud was studying engineering, but Betty's major probably wasn't specified. I'd like to think she studied civil engineering, since she joined a school-sponsored county surveying crew while still in high school.

The whole college/university thing is another inconsistency. Early in the third season the Andersons visited Jim and Margaret's old alma mater, State. It was clearly out of town, and Jim and Margaret wanted Betty to go there. She rebelled and and decided to go to Springfield J.C.

At some point the Junior College name was dropped, and Betty was attending the local college, and so was Bud in the 6th season. And in a few episodes it was kinda sorta hinted at that Jim and I suppose Margaret went there too. I guess we'd have to think Jim studied business admin. and Margaret majored in home economics.

So it's implied that Betty transferred out of the Junior college after her sophomore year?
It sounds like its similar to when Margaret was learning to drive after she had been driving for years.

You'd have to think she transferred to a local, unspecified university. I think Bud supposedly goes there too, in the final season. That would lead you to believe it's a full, 4 year college.

We could also theorize that Springfield JC converted to a 4 year college while Betty was attending.

In any case, taken all together starting with the season 3 episode, it's all an unexplained inconsistency.