If my gums don't bleed anymore when brushing/flossing, are my teeth healthier?

Yes as long as : You are brushing and flossing properly. I often get patients who tell me their gums do not bleed when they brush and floss, but upon examination, they still have some gum inflammation and pocketing. However, if your gums were previously bleeding and now are not, i would guess that they are healthy. Your dentist can check and tell you for sure.

Sounds good: Well maybe your gums are healthier but the teeth may or may not be. Sounds like you have your gums under control but just remember just because there isn't bleeding doesn't mean everything is ok? Some people with thick and fibrous gums don't get bleeding see a periodontist to properly evaluate.