All you will do is make the Bermuda angry. Yes the Rye will die off next spring when the weather warms up.

Yes, if you're going to overseed bermudagrass, you should go with perennial ryegrass. It has a much better look. It probably will not die off until May-June, depending on where you are located. Remember that the Spring is when ryegrass is growing at its best, so it will be competing with the bermuda when the bermuda is coming out of dormancy. Lower mowing and heat will help the bermuda to eventually gain the advantage over the ryegrass. If you mow high in the Spring, the ryegrass will out-compete the bermuda, and you will not like the result. The ryegrass will eventually die off from summer heat, but the bermuda will be thin and spotty at best. It's one of the reasons I prefer to not overseed in the winter; not to mention the extra mowing and fertilizer that is needed.

Thanks for the responses. Yeah, perenninal rye is tuff to find in the big box stores around my area. I think my local lesco has some the last time i checked. I am located in the Hickory, NC area.

If you live in NC you do not want to over seed your Bermuda.