That's a good question. I only ever told my mum (I live with my parents), which was very difficult but it turned out she had suspected it already. I had to tell her because I had used a pyjama shirt to clean up the blood with the intention to throw it away after, but it turned out that pyjama shirt belonged to my sister and she wanted it back.. so it needed to be washed.
I've never had to tell her "I SIed x days ago" or something like that. Just a couple of days ago she asked me a question that led me to reveal 'recent' (2 months ago) SI: the answer to her question was "to cover up SI scars [on my foreleg] so they don't shock my sister" and she was like "I thought you only had scars on your thigh" and I said "Yeah, that used to be the case."

I hope the Wellbutrin works out for you.