Mtrude:
I had my inner gearbox cover off recently but didn't pay much attention to the bushing you're referring to as I didn't have to replace it. The bushing is likely beveled on one end to allow easier insertion into the cover. I'd insert it bevel-end first. Be gentle as the bushing is soft. It should be an interference fit. I would install it at the same depth as the old cover.
Also, while you have it all apart, consider upgrading the mainshaft bearing to a partially sealed unit (6303 2RS with seal removed from one side). This will allow you to use gear oil instead of 00 grease. I've found that my gearbox shifts more smoothly with 80W140 gear oil than with grease!
My gearbox is right-hand shift, too, and I really like it! I takes a little getting used to shifting with one's right foot, memorizing the shift pattern, and remembering to match the engine speed to the gear you're upshifting or downshifting to but, once you do so, you'll probably find that it shifts nicely (assuming you have your shifter ratchet assy. and detent plunger adjusted properly)!
Hope this helps!
Al