It depends on the type (internal or external), and how bad. I had external thrombosed this past winter brought on by shoveling snow. The colon and rectal surgeon I saw recommend seeing if they would shrink on their own and recommended hot baths or sitz baths several times a day. They were shrinking nicely until the next snow storm which caused more to pop out further down the vain so at that point he (and I) decided to surgically remove them ( hemorrhoidectomy). The procedure was uneventful, but the next two weeks were extremely unpleasant. It was unpleasant enough that if I had it to do over I might give them a better chance to shrink on their own. For internal on the other hand (according to my surgeon) if they are such that they can be removed by the rubber band ligation method it is virtually painless with no recovery time needed (I wouldn't know).
Obviously since mine happened during the worst of winter I wouldn't know how it would have been trying to ride a bike while I had them (I have a trainer now, but didn't last winter), but I do know after the surgery it would have been at least 3 weeks before I would have considered trying. Bottom line is hemorrhoids come in many different types, locations, and severity of attack with many different treatments available and my experience is only related to external that became thrombosed and were removed via hemorrhoidectomy (which I would consider a treatment of last resort).