I don't honestly see that either option is bad. I think they're kind of the same thing. Either way they are kind of deciding. If you tell them you need space, they can still decide to tell you no. But in my opinion, distancing yourself because of depression is never a good thing. It's hard either way and I know how you feel about being a burden. I always felt that way. It was only recently that I was able to open up to people and trust them and I'm extremely grateful to each and every one of them now. If they care about you at all, you are NOT a burden.