Given lack of information in your question, I'm going to make a couple of assumptions; a 40lbs kettlebell isn't a significant portion of your bodyweight, it's the initial roll to elbow that you're struggling with for the TGU and you can do a set of 10 single arm swings with it.
For the Turkish Get Up, this is almost certainly a technique issue. A lot of people misunderstand the driving force when trying to do the roll to elbow portion of the TGU; they imagine it as a crunch with a kettlebell held overhead, whereas it's actually a combination of a push from the bent leg and pull from the elbow of the non-weight bearing arm.
The way to think of it is that the bent leg is pushing to roll you onto your side, while at the same time, the non-weight bearing arm is pulling to lift your body up until you're on your elbow (you can drill this later part by having something to pull on with the non-weight bearing arm). Mark Wildman has a pretty good video on this first part of the movement.
For the snatch, my first question would actually be why do you want to snatch? You can get a lot of benefit with the humble kettlebell swing (given that you're a cyclist, the glute strength from the swing will really help) without adding in the learning jump for the snatch. But, that wasn't your question, so...
The teaching for the snatch has actually changed over the past few years; whereas it used to be taught as a swing that finishes overhead, it's now taught as a clean that finishes overhead, the main difference between the two movements being that with a swing, you keep your arm straight, with the clean, you keep it tucked by your side.
The kettlebell movements all kind of build on one another, so your single arm swing will help you with your clean. A solid clean gets the weight in position to learn the press, and once you've got a solid clean and press, the snatch is only a small jump away.
That is how I'd suggest learning, and building the strength up to snatch a 40lbs kettlebell. Get your 1 arm swings solid, to the point you almost find them boring. Then concentrate on the clean and press until you're completely comfortable with the weight in the overhead position (I can highly recommend ladders for this).
Once you've got those two movements down, then you should be ready to try snatching. If you still don't feel ready, then you can break it down into two different movements (half snatches), either snatch the weight overhead and lower it as you would in a clean and press, or clean and press the weight overhead and lower it as you would a snatch.
(Note: I train hardstyle, there is a difference if you're looking at more of a kettlebell sport style snatch, but I don't yet have enough experience to talk about that sport style snatch technique)