I usually find I have to ride annoyingly slowly for it to count the distance for hatching eggs and such, but it is still much faster than walking. Once you figure out the pace, though, it works well for adding up the kilometers, but isn't really fast enough to feel like exercise. If you ride quickly enough to get your heart pumping, you will get the "too fast" message. It's also fairly easy to catch most things one-handed, but some types are too far away and require stopping to use both hands.
It's pretty easy to pay enough attention to where you're going, so I've never fallen over or run into anything, although some idiot did almost run me over a week or two ago. Riding along a narrow two-lane road with no shoulder that typically has light traffic, an usually long string of cars started passing by going the other direction. Normally I glance back quite often to see if anyone is approaching from behind me, but that section of road wasn't in the best shape, and I was watching to make sure none of the cars tried to pass each other right in front of me, so I was facing forward the entire time. Then out of nowhere, this little blue car goes shooting past from behind, in the same lane I was in, while all the other cars were still right there in the opposite lane. Even where I was at the edge of the road, I don't think there was more than one foot of space between me and that car, and I didn't even hear it coming over all the other cars going the other direction. If I'd even wobbled a little to avoid a pothole or something, that moron would have slammed right into me, because they couldn't wait ten seconds for the other cars to go by. You'll also occasionally see the sorts of drivers who intentionally blow exhaust at you or rev their engines as loudly as they can right as they pass you, to blast your ears, but that's pretty rare.
So yeah, if you're going to play by bike, be sure to take roads with little traffic, know when to ignore the game, and keep an eye out for reckless idiots. As long as you use some caution, biking is usually a pretty good way to play the game. I randomly stumbled across the only Unown and Togetic I've ever seen while riding my bike, both things I would have driven right past in a car.