Personally I would have no problems with my husband going out for a bike ride with another woman - I trust him. I had even nicknamed one of his female work collegues his "work wife" because he used to spend so much time with her work. When I met her for the first time, (she stayed the night at our home), within 10 minutes she & I were talking tents!
Similarly he has never had any problems with the male friends in my life - which given my career path, has been dominated by them (I started in IT working for an agency of the armed forces - IT (or at least my field is very male dominated - one place I worked there were 56 IT engineers and only 2 of us were female). When I was with the civil service, my gym buddies were both male soldiers (always 2 of them for no other reason than the fact that there were no female showers, and the mens toilet block with the showers had 2 entrances, so 1 on each toilet block entrance (yeh I know what you are thinking) whilst I showered). My swimming buddy at my last work place was also male - we were only allowed to swim in pairs for H&S reasons and we swam each and every day in the school swimming pool. And occationally I get to cycle with other people, usually men. In fact, I think I can interact better in person with men than I can with people of the same sex as me - female, for some reason I find it easier. Ironically I grew up without a father! maybe that had something to do with it, I don't know, but what it all comes down to is:
trust
and it works both ways. May be that is why my husband and I are more like best friends than lovers - we trust each other.