I think your last line says it all. In fact, I dated a couple women (at different times of course) during my no car days... married one of them... and she even kicked me out of her apartment one night at midnight... one of those early relationship things. Rode my unlit beach cruiser all the way home in the dark... some 14 miles. We still laugh about it.

A bit of planning and forethought has to take place... item one is ensuring that she knows you do not drive, you only ride a bike. That may just be part of your "alluring charm." Then make plans to first meet at places you can easily ride to without needing a shower... local art and music shows, small charming local restuarants. (no point in turning her off by arriving as a sweaty mess) I knew this local guy that rode a penny farthing in period dress to "special occasions;" it really was charming and "too cool." Of course he lived in a part of town that had lots of small shops, restuarants and galleries... so it really worked for him.

Later either she rides and you go together, or she drives and you ride to her place first (at a certain point showers at her place become "OK") or she picks you up. Big evenings can be done by taxi or better yet, rented limos... (no woman can resist being picked up in a rented limo).

There really is no reason that two people can't have a long wonderful relationship on two wheels. (or really a pair of two wheels) Complications may arise much later after the birth of a child... But that is a far distant bridge to cross much later...

BTW that woman I married... I loaned her money to buy a bike.... we later did several long rides together as part of our "courting." Just the other day we were joking... she still hasn't paid me back. (20+ years )