Which of the following powders would give me the highest load density in the 25-06. IMR 4350, IMR 4831, H4831, R22. I'm using the Speer 100 gr BTSP.

Of the powders you have listed H 4831 or RL 22 would give you the highest load density since they are the slowest burning of the bunch.

Does burn rate correlate with bulk? I'm assuming a bulkier powder will fill more of the case even if the weight is the same. Does anyone list load density in their loading manuals?

The Nosler #4 Manual shows load densities:

for a 25/06, 100gr bullet, MAX LOADS:

IMR 4350; 51gr; load density: 79%; 3353fps
IMR4831; 53.5gr; load density: 83%; 3290 fps

RL22 and H4831 are not listed

for reference, the slowest listed powder is
IMR7828; 56.5 gr; load denisty: 88% 3252fps

Thanks