Welcome to the world of turtle keepers! Yes, keeping an aquatic turtle is pretty involved - at the beginning. Once you get a good setup, then it's easy. The key is getting good equipment and providing plenty of space right from the beginning.
And yes, it takes new turtles awhile to get comfortable enough in a new setting to bask. It can take a couple of weeks. Then, they may first bask when they think no one is looking. You may first know about it when you walk into the room unexpectedly and hear a little "plop". Also, you can try leaving sometime (like a pellet of food) on the basking platform and if, when you come back later, it's been moved, then you'll know they've been basking.
Eventually, they will get so comfortable in their new home that, not only will they bask in front of you, they will let you pick them up right off the basking platform. But this will probably take a few years.
