This might be a weird idea, but I'll throw it out there:
Rather than try to hide the bruises (which would seem to make the problem a bigger deal than it is), would it be possible for you and your husband to deliberately inspect your bruises together when you come home? (Or maybe the next day?) Could you make it a sort of loving ritual that you two do together? Something that would happen regularly and not be a surprise?
This could be way to build connection and emotional intimacy around your bruising. Like, maybe he could kiss your bruises tenderly in a way that reaffirms your love for each other each time you come home. (But not as sex play; it's not going to be arousing for your husband to see those bruises).
I know the sight of your bruises must be physically nauseating and horrifying for him, but maybe over time he could learn to feel differently about it. Like, what if you were a boxer and getting bruised was just a part of your life? A boxer's partner might lovingly inspect her body after each fight, and help her put salve on the bruises, etc.
That way your bruises would become less about your other lover than about your husband learning to understand an important part of you.
As a woman finally getting to explore my long-repressed kinky side, I sympathize with you and where you're coming from, and all the new emotions you are having.
But as someone who is way on the vanilla side of kinky, and is pretty weirded out by hard-core BDSM, especially S&M, I sympathize with your husband and get where he is coming from. At the very least, it must be creepy to see bruises on one's partner.
Single, straight, female, solo, non-monogamous.