Never used a bolt action shotgun hunting, but it should shoot pretty much like the rest (I've used single shots, pumps, and autos).
No info on the tri-ball, but I have used regular 3" 00 and 000 quite a bit deer hunting. Down here in the south dog driving for deer is extremely popular (I started dog hunting 4 or 5 years before I got into still hunting), and with dog driving you're required to use buckshot. Range is a LOT shorter than what you're going to get with a rifle, but if you keep your shots at around 35 yards or under, 12 ga 3" 00 will do wonders on deer. Generally take the same shots as a rifle - kill zone right behind the front shoulder (or in the neck if you prefer - most that I've shot in the neck dropped right where they stood).
As a matter of fact the first deer I ever took was with 20ga #3 Buckshot out of a single shot NEF Pardner. I was 9 years old at the time. That's the only deer I got with the 20ga before moving up to 12ga, but even with those shells he didn't make it but about 40-50 yards before going down.
As to your gun being 2 3/4" only - it shouldn't be a big problem. I know a lot of people that hunt with 2 3/4" buckshot on those dog drives and they do fine. My dad uses a 1970's vintage Remington 870 Wingmaster which is also 2 3/4" only and he's never noticed any problems - just a few less pellets (he normally uses the 00 magnum loads or #1 loads). He even owns several other guns that can shoot 3" shells but has always preferred to stick with his old 870.
