Welcome to GardenWeb! I'm pretty sure Bermuda grass doesn't grow in zone 6, I wonder if you have a nutsedge infestation? A picture might help if you need your weed ID'ed, and pictures of the area might give us a better idea on how to approach the situation.

I know you won't like this but I really think you should try to get as much of that weed barrier out of your yard first, that will make dealing with the weeds so much easier.

Just remember, one day you'll look back at this and laugh. Keep your chin up.

You can limp along trying to do "something" and always have a difficult time, or you can solve the problem for real, dig it all out, the barrier and the weeds. At that point, a smother layer of paper/cardboard might be a good idea, then some mulch. If you'd like to read more options and ideas, I offered another person the same advice I'd offer you, although that person doesn't have a weed barrier to deal with. Other GW discussion.

Does your bed have a border/barrier around the edges? Whatever kind of grass it is, sounds like it's a creeper. Without some type of barrier to stop the roots, that you can tend with a weed edger to stop above-ground creeping, is necessary or it will constantly creep into the bed.

Thanks for the thoughts... I'm going to get out there this morning for The Great Weed Slaughter of 2013 and follow up with the cardboard layer and a barrier for the edge.

I feel your pain, have had to do this when I encountered it in beds before too. Good luck! At least it's good exercise...