I personally don't use an 06 but have a some buddies who do and buy OTC ammo. Choices range on what they use anything from 150gr to 180 and bullet styles across the map dependant on their situation. For OTC ammo I'd take a look at Hornady Custom Ammo in the 150 Gr Version - Spire Point or 150 Gr Interbond both should do the job. Stepping up a bit if you wish for the close distance likelyhood in grain size wouldn't hurt anything either something in the 165 gr should get the job done nicely. Lots of bullets to choose both plain jane(if you will) like the corelokt, powerpoint,etc or premium bullets...just find the one that shoots the best for your situation and put her in the boiler room!

Best of Luck