As someone who has lived through the “s/he’s learning to ride a bike” phase three times now, I’ll second what Dinsdale said about doing it in a parking lot. Find a nice big one, with no cars to bump into.
Also, second all the other voices saying “Training wheels are worse than useless”. The way to go is the hand on the back of the bike seat, trotting up and down for about 20 minutes, lots of encouragement, and suddenly, “By George, I think he’s got it!”
I’m guessing that your Ten, KVS, is expressing her anxiety about falling over, since she’s probably already realized that the faster you’re going, the harder you hit when you fall and the worse the resultant scrape. So her solution to this is to just not go fast at all. You let go of the bike, and instead of zooming off, she stops pedaling and racks it up in relatively safe slo-mo.
So invest in some knee and elbow pads for her.
Also, stock up on those big 4" x 4" Steri-Pads (and first aid tape, and a pair of scissors to cut the tape) for the inevitable elbow and knee scrapes when the kid turns out to not quite have it yet and racks it up. It’s always a huge shallow scrape at the side of the knee and elbow, and regular Band-Aids don’t work–they aren’t big enough, popping off as soon as the kid flexes the joint. You need a big Steri-Pad and about 12" of first aid tape.
Wash the ouchie, gently, under running water with a little soap (this will sting but hey, those are the breaks, and I use a tiny squirt of dish soap instead of trying to use bar soap–you want to avoid touching the ouchie), to get the grit out of it (“honey, we have to get the DIRT out of it…”) You can do the old-fashioned merthiolate/mercurochrome thing if you want, but here’s the most important part–LET IT AIR DRY BEFORE YOU PUT THE PAD OVER IT. Otherwise the next day you have the pad stuck to the ouchie, which HURTS to get it off (soak it off if you find yourself in this position).
Also, using that antibiotic ointment on a still-wet wound is actually counter-productive, as the wound won’t make a good hard healing scab if it’s shut off from the air by a layer of ointment. The next day you’ll have a sloppy, oozing mess instead of a good scab. So let it air-dry first. Also, squeeze the blob of ointment onto the pad, not onto the tender wound, which proposal invariably produces hysterics after already having gone through the traumatic “washing” experience (“don’t touch it, don’t touch it!”)