Playing with records is easy, but still good practice. Your best bet though is to download some drumless music - you can find tons of it for free all over the net. Check Youtube, and rip them using youtube-mp3converter (just google it). You can usually find drumless tracks of your favorite songs.
The difference is on records you hear the drums, so you feel the pulse. But when drums are removed, you have to feel the pulse by your own means, and because most all recordings in studio these days are done with a metronome, drumless tracks are unforgiving, so the music won't give you any slack. It's a very good time keeping exercise. I think 30 minutes a day of practice - 15 minutes with a metronome, 15 minutes playing with drumless tracks, and in just a few weeks, you'd be a grooving champ.