Bullying is when someone tries to belittle you or use their power, real or otherwise, to force you to do something. Or feel bad about yourself. I used to get bullied all the time because of who my family is. Other students whose friends and family fought for the Ministry and Order made fun of me because the Lestranges were my aunt and uncle, and purebloods - well, Slytherins, mostly - made fun of me because my pureblood mother married a Muggleborn, my father. They all thought they were better than me for things I couldn't help. Bullying isn't always overt. Sometimes it's subtle, and I'm afraid that's what it is with Regulus.
Whether you're just friends or more than that, everything I've said still stands. You deserve friends who treat you with respect. I'm afraid I haven't seen any moments when Regulus has done so to you. Accepting faults is one thing; allowing yourself to be blinded to who a person really is, regardless of the mask they show you, is completely different. Like I said, the real measure of a man is how he treats those less fortunate than him, regardless of what that kind of fortune may be.