Get free-spinning bolt out of TV

Because it only takes a few seconds to drill through, is only about three inches wide, and runs vertically, It sounds like it's a metal stud (as you've found out). Metal studs are not as strong as wood studs when hanging stuff, but the one meal stud, along with the strength of the drywall should be enough to carry 20+ pounds. If it were approaching 40+ pounds, it would be better to span two metal studs.

I've had the best experience hanging items on metal studs with toggle bolts. Get the two smallest toggle bolts you can find that are: 1. Rated for at least 40 pounds each, 2. Long enough to go through the drywall and studs. Depending on how big the mounting holes for bicycle rack are, you may need to pick up some washers too. You want to put the toggle bolt through the drywall and stud. Find the center of your metal stud and drill a 1/8 inch hole at the height where your mount is going. Then, make the hole progressively larger until the toggle fits through. Then, just follow the instructions that came with the bolts as if you were putting them just through drywall.

When the two members are not touching, the bolt starts to act as a "cantilevered beam" (as you have alluded to) and you hit a point where it is not the shear value that governs, it is the moment (bending). You get additional support by the cleat trying to go down and into the wall which puts withdrawel load on the fastener effectively adding more support using the tensile strength of the fastener.

As a note standard zinc hardware store bolts are ungraded steel usually with no actual values assigned to them.

First, if you have the time, you might try to buy some graded bolts online or from a local supplier; not necessarily a high grade, just graded at all so them meet a minimum requirement for strength. Or use structural screws such as Simpson SDS screws.

Secondly, if you have effectively 1-1/4" of cantilever, I would recommend slightly more embedment into the stud. If you hold things flush to the wall with only a 1-1/4" cantilever, I would up the embedment to a minimum of 2-1/2" or more to ensure the wood stud does not crush at bolt under load due to the multiplying effect of the cantilever. Visualize a 12" long bolt embeded 1" in to a 2x4, the wood crushes on the 2x4, the hole enlarges, and the bolt comes out; the bolt does not necessarily even bend before failing. An increased embedment also increases the amount of withdrawal load the fastener can handle when it slides down the wall (if the bolt does bend) and tries to pull out.

Another option is to simply get more fasteners per stud. You can do this by upping the size of the cleat to a 2x6 and use two or three bolts. Or you can add a vertical member below the cleat at each stud and effectively add a bolt every 4" or so in the vertical member with predrilled holes plus the bolt(s) into the cleat. Key is more embedment and/or more bolts to handle the cantilever.

Or, just build them free standing.