If you want to put large hole through a structural member like a stud then you should be strengthening it around the hole. Personally, I'd do that even it wasn't a load bearing wall though obviously if it is, then it becomes a lot more critical.

The easiest way to deal with it would be to fit a stiffener plate like this to the stud before drilling the hole - Obviously you'll have to find a local equivalent and will also have to remove the drywall to get access but it's probably the best bet.

Personally, I'd be looking at running the pipe down through the wall and out through the floor inside the wall then doing the extra run underneath the wall. The bottom plate of the wall is less structurally important than the studs so it's a better solution if you have access underneath and assuming there isn't a floor joist directly under where you want to run the pipe