Many here have found that young RES will not eat the first few days in a new environment. In fact, if you look at my first posts here, you'll see that's exactly what I was posting about. So no need to panic yet.
You are correct that your turtle needs to bask, but it needs more than just a place to get out of the water. It needs heat and UVB light. Both can come from expensive light bulbs that provide warmth and UVB or you can spend much less on two bulbs. The main site has a section on lighting that is very informative
http://www.redearslider.com/index_lighting_basking.htmlWhat size tank do you have your turtle in? How high is the water? Do you have a heater? A filter?
If the water temp is too low or the basking area not warm enough, that could also influence appetite.
Welcome to the site. You'll find a friendly group here with lots of passion and knowledge.
Don't worry if it's not eating yet. Read some of the care info on this site. Be ready to enjoy caring for your new turtle. I know I've found it to be very rewarding.