Alex65 said:
First, I don’t know what material to use or how to make the bushings between the bearings and the cylinders straight and precise without special equipment ...
You really need to find someone local who has a lathe to make the components, from either metal or timber. The type of lathe available will determine the easiest way to fabricate the machine.
If you cannot find a lathe, search 'conveyor roller' on a website like eBay, and you may find exactly what you need, complete with axle and bearings, at a very reasonable price.
Metal tube, could be cut to length and sleeved to locate the bearings, or a disc end could be made in a metal lathe to carry the bearings.
The rollers could be made in a wood lathe, First drill an axial hole, so that a long axle can pass through without contact. The axle could be a 30" long, threaded rod. The outer bearing race will seat in a recess cut in the end of the roller. The long through axle would then position the inner races, with an external tube on the axle, or a nut on the threaded rod, to press on the inner race, to keep the bearing in the end of the roller.
Alex65 said:
Are 6202 and 6203 bearings ideal for a roller bike trainer?
The 62xx series, also 60xx, 68xx, and 69xx, are low-cost deep-groove ball bearings, which is sufficient for the application. The inner diameter needs to fit over the axle, while the outer diameter needs to be smaller than the roller diameter. Search "deep groove ball bearing" on the web to see lists of possible sizes to select from. I would expect the axle to be about 16mm (0.625") diameter.
Will you have a slave roller under the front wheel, driven by a rear roller?