I think you are entitled to refuse the invitation to be the bridesmaid, and you are entitled to keep the reason to yourself. Even if we are at our lowest regarding depression, we can empower ourselves. We are many things we don't like but we should always remember we are the owners of ourselves. Sorry my Grammar is awful but I think you understand me.
I am not an American and I don't live in your country now. I spent a lot of time (years) in your country and could appreciate lots of good things from your culture. But I think society puts a lot of pressure on people and I don't like that. It makes people too unhappy. But on the other hand, in your country I learned about the value of self-affirmation and self-determination. Humbly, i think these two things are important for us, people with depression. So many things of our depression (ideas, feelings) are related to other people's expectations, or about "what society expects from us" given our gender, age, social class, etc.
Also, I think we don't have such a freedom the culture says we have. We are tied to too many conditions and conditioning. We don't have a lot of space to mannouver. We are not really making all the choices we think we are making. But we can make some, starting by asking ourselves what we really want. I am not telling we should just impose our preferences always or disregard other people's needs, or forget about reciprocity, or not to love our neighbors.
But I think that there are many social functions and activities that we are entitled to refuse if we think they are an extra burden given our depression. In my experience, we need to be careful and not to isolate ourselves at the end of the day. But, again, sometimes forcing ourselves to do social stuff does not pay off, either to ourselves or to the other people we feel we need to please.
I am sorry if I am saying something inadequate
I wish you all the best with this