Trinity, I would scalp it, feed it, give it a deep watering, and see how much comes back. Bermudagrass is tough, but if you are gardening on the northern limits of its hardinesss range, it may have taken a hit last winter, especially if it is unimproved common bermuda. Any bare spots that are less than 3 feet across will heal themselves, but wider spots may need to be re-seeded with an improved variety, such as 'BlackJack' or 'NuMex Sahara'--they are hardier to cold than the regular stuff. Pernicious perennial weeds--such as oxalis or nutsedge--may need to be treated with chemicals.

In the long term:
Feed regularly. Bermuda can survive for long periods with no feeding, but fertilizer gives it a competitive advantage over weeds.
Water deeply, but not too often. Bermuda grows deep roots for a lawn grass, and that gives it an advantage over most weeds if the soil surface is allowed to dry out between waterings.
Mow often. Bermuda, like all lawn grasses, shouldn't have more than 1/3 of its height removed at a mowing. If you mow it at 1 in., don't let it get taller than 1 1/2 in. before you mow again. If that doesn't fit your schedule, mow higher.

Hope this helps!