I worked in the bearing industry for 5 years. The 6206 is a good part number. You can buy them online (Amazon even sells them) or a reputable bearing house ought to have them. Depending on your location, try Motion Industries, BC Bearings, US Bearings, Applied Industrial Technologies or Kaman, to name the majors. You probably also have a few locals.
Some 6200 series bearings are available with both metric and inch dimensional bores- metric is standard- so double check your shaft but it's probably metric. You will need to specify the nomenclature for whether it is open, shielded or sealed. Open means you can see the bearings inside, shielded means the bearings are covered by a metal shield but that water and contaminants can get in, and sealed means the bearings are covered by a rubber seal that keeps all contaminants out and the grease in. So if it's open, it's just a 6206. If it's shielded, it's a 6206 2Z and if it's sealed it's a 6206 2RS.
FYI- some manufacturers like MRC and FAG drop the 6 and just call this bearing a 206.
Good luck.