I have gone with a longer and thinner than average stuff sack and a couple cheap straps (Coughlins). The straps were their "sleeping bag straps" and were about $2. The stuff sack was one that a tent came in. I wanted a bit of space between the bag and the bars so I used short pieces of pvc pipe as spacers. The straps went through the pipe, around the bar, and around the bag. It worked great and was essentially free since I always have some spare straps on hand and the bag was a tent bag that I had.

I have done a similar setup with the same straps but with a bundle of gear rolled up in my tarp. That worked fine as well.

In a couple cases I strapped a little camera bag on the bundle for quick access. It also contained my phone, money, plastic, and ID.

I have also used traditional handlebar bags, but they are more suited to stuff like cameras, phones, and other small items you want handy. I like the Nashbar Elite bag pretty well and it was inexpensive.