Don't get a bike rack that clips, tightens, etc. on any part of the frame. New frames are very thin and they will eventually rub, break, etc. your frame (unless you are using a steel, low end bike). If you've ever seen an alum. frame cut in half, they aren't much thicker than an alum. can on some of the tubes.
Get a rack that clamps the wheels down (or over one wheel) and then clamps around the rim of the rims. You can get (like other stated) versions with will swing out, etc.
We put a step in our hitch first, then the rack extends out of the step. We carry 2 bikes and it does extend out pretty far. We put the flags, etc. on the outside bike.
Thule, Yakima, etc. all make various racks like I'm mentioning. Here's a link to one of the model designs I'm talking about:
https://www.thule.com/en-us/us/bike-rack/hitch-bike-racks/thule-t2-pro-xt-2---21691037
They are terribly expensive but check craigslist, etc. There are other brands too. Also, there's an extension for these with 2 more mounts. We don't use that on our camper but use it on mtn bike trips where we don't take the camper (a different car, truck, etc.). We actually made it ourselves using extra mounts we had and we built up the extension and cross members and bolted the mounts on that. Save used a few hundred dollars and we had them as replacements from Yakima from our original purchase (one was missing a screw hole (I just tapped it out) and one the arm wouldn't stay up).