I would say that if you only have two weeks, it is definitely not worth doing--just too far. And regardless of how much time you have, this is kind of a big trip for your girlfriend, as a first moto trip...of course I don't know her at all, but if it turns out she's not having fun, you should definitely have a Plan B...

I would not be worried at all about going to Russia, I expect that you'll love it. But if you just gun it down the major highways, it will be a pretty miserable experience--lots of trucks, police, traffic, etc. Better to take your time and take the side roads through the little towns--but at that pace it would probably take you five days or so to get to Tbilisi from Tallin, and that's if you don't decide to spend a day somewhere.

Unless you want to take the ferry from Odessa to Georgia, you won't be able to get to Tbilisi via Ukraine, at least without going through Russia; given the situation in Donbas, you'd need to cross into Russia around Kharkov.

Moscow is an amazing city, but the traffic, and traffic flow, is not for the faint at heart. I would give it a pass unless you really want to see it for some reason. If you go there, plan to spend at least a couple of days there, and stay in the center, or there is no point in going at all.

Where to stay is kind of interesting...I never made reservations, or even looked for places in advance, and usually found a nice place in a decent town or city. Personally I prefer cities so would try to plan the days to spend the night in one of the many small cities, and then spend the afternoon and evening walking around town. Smaller towns are very hit-or-miss--some are amazing, others are dumps. If you're coming from Latvia, I highly recommend that you spend the first night in Russia at Sebezh, a little town on a lake not far from the Latvian border. Nice little town with craft outlet right by the lake, it was great.

Anyway, let me know if you have more questions, be happy to answer.