You don’t need to spend six years. Bioengineering is an ABET-accredited 4yr Bachelor’s degree in Engineering leading to state licensure, so there are some core courses that reduce transfer flexibility. (Bioengineering is also offered at the Master’s level). You’re really better off just transferring to the right school as soon as possible.

Incidentally, Bioengineering is just one of several names for related branches of Engineering. You can find accredited programs under the following names:
Bioengineeering
Biological Engineering
Bioprocess Engineering

(Bioprocess Engineering might be the next big field in Engineering)