The same happened to mine and a lot of other people who ordered the bundle. This exact problem caused me to lose the final boss fight as Ventus where you have to spin the nub and spam "X." Someone told me to turn the PSP upside down (screen facing floor) for a few seconds so that the UMD could be read easier. With that advice, I tried it and it worked. The problem hasn't occured since (BBS is my only PSP game, so I'm not sure if the same pertains to other games or if you have to turn it upside down whenever you put in a new UMD).
My cuz says that his PSP-3000 (piano black) and mine (bundle Mystic Silver) have a different material made up on the back. My idea is that this may cause the game UMD slot not to close or allow the UMD to sit properly. Mine's been okay the past day or two, but if you have your GS reciept, see if you can get your PSP exchanged. There are other threads about this situation (one started by me), so feel free to browse those.
Good Luck!