I would definitely not recommend doing this in a letter or even on Skype.
Something this personal should be done face-to-face, so that you can gauge reactions, and maybe stop early if you realise that things aren't going well - cut your losses, as it were.
Also, don't make it one-sided. Ask her how she feels about the two of you, and what she could imagine happening.
And yes, do it sober, in a safe, neutral space for you all.
"Listen, or your tongue will make you deaf." - Native American Proverb