Dear {Name},
I feel terrible for so rudely ignoring you the other day. I allowed myself to be distracted by my phone, by things I thought were important at the time but in retrospect could have waited. I should have been focused on the real-life people in the room with me. It wasn't until I got home and thought back on the {evening/event} that I fully processed how my inattention was likely interpreted.
I'm looking forward to seeing you at {future event}. I promise my phone will be put away and you will have my full attention.
Sincerely,
{Name}
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