For the bike following shots, I would also recommend a GoPro or DLSR depending on what kind of shot you are looking for.
If the slight fish-eye is OK, you have good lighting (sunny day), and can tolerate some movement, the GoPro will probably be the easiest and cheapest. I would personally mount it on a handheld stick so you can get really close ot the subjects. I took some ski footage recently with a GoPro on a handheld stick while skiing around my subjects, and it came out amazing, because I could grab really odd camera angles (i.e. right next to my boot, over the head, between my legs, behind me as well as transitions) as well as get really close to subjects I was skiing next to. Hold it upside down to provide some stability. It had some shake, but not as much as you might think. So my first approach would be to mount the go-pro on a stick mount (telescopic one from Amazon for $15 or so), get on a bike behind them and shoot some footage with one hand and see if that is good enough.
Option B is to mount a DLSR, which has no fish eye and also better lens reach, onto another bike or car. Since this is too heavy to handle with one hand on a bike, you are probably going to need a car, truck or a two person bike. Also if you go with the longer lens, then you need to worry about steadying it - so we're into some kind of stabilizer. I'm thinking a DLSR mounted on a handheld steadycam or stabilizer held out the passenger window (or back of the truck) while someone else drives.
Safety is a concern in both approaches as well, so select a location that is flat, smooth, slow and out of traffic. You can always speed up the final footage a bit in post if needed.