"Please Please Me" is pretty easy on bass and it's lots of fun to play. I'd also recommend "All My Lovin'" and "Eight Days a Week" as being fairly easy, but not boring. If you want really really easy, you can go for "Love Me Do", but it's so easy you might fall asleep half way through it.
"Maxwell's Silver Hammer" is pretty easy and fun to play. After you've practiced a bit, take on "Come Together", which is fairly easy because once you learn the basic riff, that's all there is to it.