There are two simple options for the bearing
The first is to suspend the bob from a flexible cord passing through a fairly tight grommet so it will maintain a constant point of contact in all directions.
Another option is to get a large ball bearing, ideally plastic or unhardened (or at least not through hardened) steel and then drill and tap it for an attachment point for your pendulum (or weld a nut to it in which case 316 stainless is a good option.
You can then mount this in a plate with a hole of something like 95% of the diameter of the bearing, for this slip-on pipe flanges are convenient. To get the best possible bearing surface fit you can lap the ball into the join with valve grinding paste or similar.
The example below is a slightly more complex version and can be locked made from a 50mm diameter 316 stainless ball bearing and a 1/1/2" bsp pipe flange. These flanges are failry thick but if you chamfer the top edge of the hole it gives you a bit more clearance and it can act as a reservoir for grease.
Edit to address questions in the commenst :
1) For a grommet or collet type support monofilament rather than braided wire might be best as the tension in braided wire might mean it behaves slightly differently in differnt directions.
2) For the ball bearing option it might be easiest to weld a nut to the bearing (or drill and tap for a stud) and thread the end of a round bar to fit. Idally you want the connection to the ball to be fairly rigid or there is little point using the ball at all.
3) There is probably no advantage in going for a very heavy ball as more weight will only increase the friction at the bearing surface having said that a larger ball give syou a larger range of movement. In my example a 50mm ball in a 48mm beveled hole gives around 45 degrees of motion in all directions from vertical. With this approach you are not relying on the felxibility of a 'string' of provide the range of mevement so you have more options in how you attach the bob to the bearing whihc in turn should allow you to use a heavier bob while keeping bearing friction and damping to a minimum.
4) I would guess that the magnetic donut is providing an impulse to the pendulum to compensate for friction losses and keep it swinging indefintely. This requires a coil and a modified ocsillator circuit...but that probably merits a new question.