It is interesting you bring this up. I only just re-watched Explorers a few days ago (the episode where Bashir first meets Leeta as described in your post). As a doctor myself I was appalled at his lack of professionalism. Worse still he does this in full view of Quark's patrons, which could have the added effect of significantly damaging trust from the community he is meant to serve. It was so jarring it completely took me out of the episode for a while and I have not viewed Bashir in quite the same light as I used to in subsequent episodes.
I guess some might argue that a doctor should have a right to be flirtatious in his off-time and it is quite possible that Leeta is not on his patient register and thus not his patient. However, the sleaziness and public display of his conduct are definitely problematic. If he was in a faraway place and no one knew him as a doctor and his patients weren’t likely to be around I would cut him more slack but this was definitely not the case in this scenario and he should have had that awareness.
I don't remember Melora and Crystalis well enough but from what you are saying it sounds like they would not be compatible with contemporary standards about how a medic should behave. If he indeed infringed upon a competent patient's right to decide or abused his influence over them, trying to groom romantic relationships, he would face a severe caution, suspension or even a loss of his licence to practice should someone raise concerns about him to the medical professional body.
He was also often quite happy to discuss patients' private medical issues in the middle of Quark's.