If your instincts are so dead on then why are you asking the help of a message board? Why are you hesitating? Because you care about the outcome. But you're saying you don't care about the outcome. You say you've never faltered with women before--but in your letter you say you're shy and inexperienced.
You want to express just how you feel--yet you need the help of strangers to help you accomplish that. You seem to be able to express yourself quite well without help? Don't worry about it--I do the same thing.
If you really don't care if she stays attracted to you or not, then go ahead and give her that letter, I agree you should do what you feel like doing. I was under the impression that you wanted to further this relationship with this woman romantically, but if you're cool with just friendship then that's what you should do. If you're coming from a place of confidence, and don't care about the outcome, then just do what feels right. Just know that things are going good between you ALREADY, and doing something like this has a very real chance of destroying the relationship you have built between the two of you in an extremely short time. I can't read what you wrote and NOT say this because I can it turning out wrong. I am seriously trying to save you some heartache here.
Have you considered taking her out for a nice romantic christmas dinner or something? Maybe take it up a step without pouring out all your feelings to her? And if you HAVE to tell her you love her and kill all the mystery between you two-- couldn't you tell her in PERSON at this nice romantic dinner and see the reaction in her eyes? Don't you think she'd appreciate you telling her in person more than a letter? It's not too late.
Doing this sort of thing has NEVER EVER EVER worked for me, or any of the men I know. Ever.
Hope it works out for you in any case.