As someone who's experienced this problem, I will tell you that lip liner helps, but it's not a complete solution, especially if your lips are very dry. Keeping your lips conditioned and moisturized will help cut down on the color bleed, but I'd definitely recommend the stay-put lip color too.
Cover Girl makes several kinds, if I recall. Hope that helps!
I've heard forever that lip liner keeps the color from bleeding. Also recently I've heard that some lines offer a lip foundation, though I've never investigated or tried them.
I found by using one of those stay-on lip products bleeding doesn't occur. (I use Maybelline Superstay). I use the "foot" of the applicator and line my ips, then fill it in. If you need more definition, you can then lightly line lips with liner in a matching color (NYC has some good and affordable stay-on liners). To finish, I dab some sheer face powder around the lip area. VOILA - no more unsightly bleeding lips...hope this helps.