1" diameter or larger bamboo should work. You can use anything. Most old timers I know go out in the woods and find broken branches to use.
I've used old lumber ripped down to 1" squares.
I've put up teepees as short as 4ft (cause thats all I had) and had good luck, but I prefer anything over 5ft.
I wouldn't go any higher than I was comfortable reaching. As far as bamboo being strong enough it depends on the bamboo and the way it it constructed. They make large scaffolds out of bamboo in the Orient. If it seems like it wants to bend too much,make each piece run more vertical, put cross braces about half way, use two or more piece parallel and bind them together.
I would use 2x2s about 8 ft long and that should give you all the support that you will need, in a TP shape. In the garden for the past few years I have planted the beans in 30ft rows with 2x2s driven into the ground every 8-10 ft. then I make a string trellis tied between the posts. This puts the plants at least 6ft in the air and usually they are still trying to go higher. This year I will be using the same method only will be purchasing 10ft 2x4s with the string trellis going betweent them. The reason for the 2x4 is the new height that we will allow the plants to grow. Every year by planting two rows side by side 5 ft apart allows the plants to grow together at the top. In this way we can pick beans on the sides and the top by reaching up. We try to have fun seeing just how high they can grow and usually we don't have enough height so this year I plan to pick using a ladder.
I had a 16' x 4 1/2' wire fence panel, and I drove four t-posts, bowed the fence panel up between them, raised it up one foot, and wired it to the posts. Then I added soaker hoses and planted two short rows of beans at the ends. The vines should climb up each end of the fence and meet in the middle.
The top of the arbor is 6 1/2 feet above the ground, just above my head. I planted big Romano-type pole beans on it and I know they'll hang down from the vines, so I should be able to pick beans easily while standing on the ground. I bet our grandkids will enjoy playing under this arbor - and I know I'll enjoy having a shady place in the garden to go to this summer.