From a Christian perspective (to which I hold), it would not be right at all. Christians are to avoid even the appearance of evil so as not to bring shame upon the name of Jesus. If someone were to see me riding "alone" with a married woman, it would certainly arouse suspicions of adultery, regardless of whether there was any actual adultery or tendencies toward that. So it should be avoided.

Furthermore, why on earth would a married person want to put themselves in that situation? It's only asking for trouble. Suspicions of adultery from anyone who knows either person, seeing them alone together. And it's also putting oneself in an environment which could easily lead to adultery.

I wouldn't do it. Not regularly, or even once. I'd choose to ride alone or with at least a group of three.