A bunch of random observations:
I've got one of those cheap Chinese Bigsby clones. It has plastic bushings. That's where I'd start.
If you want to do rolling element bearings, use needle bearings. In ball bearings, the diameter of the balls are typically much larger than the diameter of the pins/rods/needles in needle bearings. That make the bearing outside diameter, and the housing that holds it larger, and the inside diameter, the tube holding the strings, smaller.
The other knock against ball bearings is that contact area on the inside and outside races are points. Needle bearing have a line contact, spreading the load out over a larger area.
Think about how this bearing is going to be loaded. Most of the time, the tremolo isn't moving. All the string tension is acting on the same couple of balls, pushing down on the same location of the races. When you use the trem, the balls move, but, go back to the same spot. You can wear spots into the races.
On bicycle headsets, they call that index steering. When you turn the handlebars, you can feel little detents in the steering, when the balls drop into the next worn spot in the races. High end bicycle head sets use ball bearings at the top, and tapered roller bearings at the bottom, to avoid that. In highly loaded, small excursion joints, they make special precessing bearings that move freely in one direction and then skate a little in the other direction, to distribute the work over more balls/rollers, and work different parts of the races. Naturally, precessing bearings are much more expensive.
In your pic, the pivot supports are separate. They're going to be screwed into wood and then support the tube and react string and trem loads. The wood isn't super rigid (especially through a screw) and it expands and contracts with heat and humidity. You might end up with more movement on either end of the tube than you'd like.
The loads you apply on those pivot supports are going to be different. When you press down on the trem arm, it's pushing down on the spring and trying to pry that nearest pivot off the guitar. The other pivot is going to be reacting string tension through the tube, pulling it forward.
Bigsby's design, where both pivots are part of the same casting, reduces relative motion between the two pivots and it react the trem arm load over more fastener.
None of the things I mentioned are fatal design flaws. You just need to pay attention to them and beef up your design where it's needed.