What you're describing does exist, it's called a delayed action closer. They're common on commercial and fire doors where you want the door to stay open for a bit, then close on its own. The catch is they're pricier than the basic surface closer on your door and most hardware stores don't stock them on the shelf, you'd be ordering one online. There are also hold-open closers that latch at around 90 degrees and only release when you give the door a firm push. Either of those would solve your bike problem, but they're a bigger job than most people want for a side door.
Honestly, the simpler fix for your situation is a kick-down door stop. It's a small bracket mounted low on the door with a foot pedal. Roll up, kick the pedal down with your toe, the door stays put, wheel the bike through, then kick the pedal back up or just nudge the door and the closer takes over. Since your foot is free while you're steering the bike, it fits your routine better than anything that needs a hand. About those little adjusters on the arm of your current closer, those control closing speed, not wheather it parks. You can slow the door down so it drifts shut gently, but it'll never sit open for you. Some closers also have a seperate latch speed screw so the final couple of inches don't slam. Worth tuning those anyway so the door isn't yanking itself shut the moment you let go. One more low-tech option since someone mentioned the rope trick: I use a hook-and-eye on my garage door for the same reason. Eye screw into the wall stud, a short length of rope with a loop on each end, slip one loop over a hook on the door and the other over the wall eye when I need it open. Costs a couple dollars. The downside is remembering to unhook it before the door slams, and with an exterior door you do want to build the habit of checking it every time, expecially in winter. If I were doing your door from scratch, I'd fit a decent sized closer with adjustable sweep and latch speed, plus a kick-down stop. Best of both worlds.