A couple things I'd suggest reconsidering.  First, it's a false dichotomy that this was done "...while roads go unpaved," as the money that put this program together came from a combination of a federal grant earmarked for bikeshare and corporate sponsorship for bikeshare.  It wasn't as if the PBOT or ODOT were sitting on a pile of cash and trying to choose.

Secondly, a successful bikeshare program reduces the road maintenance backlog.  Any trips done by bike that would otherwise have been done by car or bus are a net reduction in road wear.  Further, any increase in cycling overall as a result of bikeshare, e.g., people becoming more comfortable biking and riding their own bicycles more often, is a further reduction in road maintenance.  

The addition of this new public transportation option to the central city -- an option that requires no tax input for operations whatsoever -- is likely to be a net positive for road maintenance.