How much college math they give you credit for depends on the school. Cal, for example, gives credit for math 1A & 1B if you pass the Calculus BC exam. Other UCs, such as UCLA or Davis, give 8 units credit which is 2 quarters worth of math, not 3 (a full year). Since the OP hasn’t said he is a CA resident, it is worth looking into the credit at the schools she/he is thinking about.
I’d also say that Calc BC goes at a slower pace than college. At UCLA, for example, the 2 quarters of math classes take 20 weeks. Subtract off “dead” week, the 10th week of classes which are traditionally used for review and summation, and that’s 18 weeks. In HS you’ll take the AP tests in May, so you’ve had about 35 weeks of class. The difference is even more stark if you look at class hours. A UC class will meet for 1 hour 3x a week; a HS class meets daily. So the material covered in 54 hours of instruction (heck, use the 10th week and make it 60 hours) is covered in 175 hours of instruction in HS.