One more unusual one to add, a Lortone Rock Tumbler. It's amazing how many look-a-likes are so inferior, just get a Lortone.
https://smile.amazon.com/Lortone-3A-Single-Barrel-Tumbler/dp/B000RB16W8
Anything by lortone. They aren't thirty years with only a belt replacement.
Lol oops meant stainless steel jewelry shot. And you can make a rock tumbler for $30ish if you're only doing a little tumbling. But if you plan on doing more than 3 or 4 batches then you'd want a good one. Also the home made tumbler will be loud as hell, the one I linked to is rubber lined to help dampen sound. You wont want to run it next to your bead or anything but they are far less obtrusive.
With the proper bits, polishing paste, a rotary tool stand and an industrial rotary tool that specific agate could take hours. With just a regular old dremel, water and some crappy bits /u/ces614 is right that agate could take you days.
Source I do a lot of rotary tool work on shells, and have practiced on some small soft stones. On the Mohs scale they would fall between 3 and 5, an agate is what roughly 7 on the scale. The hardest thing I've worked on with the dremel I have is a striped fox conch, if you mesured it against the Mohs scale it would be about a 6 maybe 6.5. I was making a shell horn, it took an hour and a half total to finish it. Imagine spending an hour and half on that agate, thats if you only do one side. You'd have to take a lot of breaks even with a stand or a flex shaft. I guess if your just doing the one stone you could do it but man that's ify.
Personally just drop the $80 on a nice Lortone tumbler, they are simple and last damn near forever. Use the rotary tool, or whatever you already have to shape your agate then throw it in the tumbler. If you want to do it super cheap, buy a toy tumbler they cost about $30. After 2 or 3 sets of rocks they start to leak, unless they have improved them any since I was a kid (I'm 30 now) which I doubt.