From a distance, a person who has cuts and bruises from practicing BDSM appears to be in an abusive relationship. It's hard to tell the difference. If someone sees the wounds and asks you if you're being abused, how would you convince them otherwise?
It's almost impossible to convince people everything is okay if they see injuries on a frequent basis. It is wise to hide cuts and bruises. Think ahead of time. You don't want to push your luck when you're going swimming next week. I'm sure you know tha already though. The best way to deal with this situation is prevention. It freaks a lot of people out and it's awkward to explain, unless they're good friends and/or very open minded. Sometimes it's especially difficult to explain how a sadist can get hurt as well. With that said, you should tell the truth, if you think they'll take the news well. Sometimes I've lied about accidentally injuring myself while performing DIY. I possess DIY skills to 'support' my lie. I know it's morally wrong, but I don't usually want to waste half an hour of my life explaining sadomasochism. I feel enough guilt already and I don't need confused people making it worse. Some people are good at detecting lies, and you won't be able to lie with a straight face unless you feel as if you're being honest. For example, if it's an obvious injury, I'll carefully act out how I'm gonna lie I got it, preferably very close to the time that I actually got hurt. Then I feel confident because I'm prepared for the worst.