You 'season' a cast iron skillet. Rifle barrels are steel, not cast iron. Bore Butter does not 'season' a barrel.
It also does not rust, or cause rust. However, as a rust preventative it does leave a bit to be desired. If there is any water left in the barrel when you apply the Bore Butter it will likely remain in place and cause rust. Bore Butter won't replace that. It does not displace water. It's sole rust preventative feature is that it coats the steel to prevent oxygen from reaching the surface; if there is water present it can prevent the Bore Butter from coating the surface in that area and thus rust can occur.
I've used Bore Butter for years with no ill effects, that is, no significant or discernible rust. However, I've seen cases where rust occurred with other people's guns. In those cases they've all said they took no extra effort to remove water beyond running a dry patch after cleaning; I think that was not sufficient and the Bore Butter was thus applied on a wet surface and thus was not fully effective.
BTW, I now use Ballistol full strength and am pleased with the results. Mineral oil based solvents such as Ballistol and Butch's Bore Shine do not exhibit the problems associated with petroleum based oils.
Others use olive oil or other vegetable oils; these are short term however as they can turn rancid over the long term.