A physics degree would be the mainstream route, possibly backed up with some biology courses (although a good understanding of classical and statistical physics is probably much more important than biology). Our computational biophysics groups also employs a handful of non-physicist (a biologist, a chemist, and an engineer). But that is mostly because a lack of suitable physicists on the market, not because of an intended interdisciplinarity. Some universities formally offer specialized biophysics courses, but if your university of choice doesn't, then a "normal" physics degree is probably just as fine, too.