While I don't shoot off a bi-pod, I have heard many instances when a bi-pod on ANY rifle can effect group size and location.
I've had my 30-06 for nearly 3 yrs and I learned a few things. It doesn't like 150gr bullets as well as the heavier bullets. It will consistantly shoot .75" or less with 165gr bullets. It really likes 180gr bullets. The 2 most accurate loads out of the gun are with 180gr Nosler bullets.
Here are my load choices.
Winchester brass, 165 gr Hornady SST, 56grs of IMR4350, CCI 200 primers. Load the bullets to the maximum magazine length and I see 2800fps. The gun seems to shoot any good 165gr bullet well, but the Hornady SST and BTSP are the best.
Military cases, 180gr Nosler Solid Base [similar to Accubond or Ballistic tip], 60grs of H4831 or 60-61grs of Rel-22, CCI250 primers. Once again I load them to the maximum magazine length and I get 2650fps with them. Those two loads will shoot under .5" and the H4831 load gave me my first one ole group with the "X" gun. It measured .274" for 3 shots. Just look at my avatar and you'll see the target.