I am US citizen and Canadian resident. I return to Montana every fall to hunt and bring ammo and guns no problem. No one has bothered me about either when crossing even during routine inspections (sometimes it's just my turn to be checked ... it's the way it works and I'm okay with that ... anything to help in the war on drugs and gun smuggling). I believe you are limited to 5000 rounds. The guys at the trap club have run into that during shoots across the border. I know that I do not require Form 6 to bring my guns across. Never been bothered for it but out of curiosity had the border folks on US side check when crossing two years ago. Even the supervisor wasn't entirely sure. She called the Seattle office. Nope, not needed. I always carry proof of ownership (bill of sale or old Long Gun Registry card) so they know origins of guns. That's a potential duty issue when returning. There is a form I can fill out on Canadian side when leaving the country but ownership documents have always sufficed. Anyway if Form 6 is not required for me to move guns back and forth, I'm not sure why you would need it.
Now there is the issue of whether non Canadians can legally purchase the ammo here. As I understand it that varies from province to province. Without a Canadian Possession and Aquisition License (PAL) you cannot purchase ammo in Ontario. But I have been told PAL is not required to buy ammo in Manitoba. Okay, so a PAL is required to PURCHASE ammo in Ontario but does that mean it's required to merely possess ammo? Unlikely because then American hunters coming up here would be limited to slingshots and bow hunting. So there seems to be some grey area re aliens picking up ammo without a PAL.
Wait ... now that I think about it Americans coming up to hunt need to obtain a temporary PAL at the border. That must allow them to buy ammo. So if coming up to shoot gophers or for a documented range shoot, Americans can get the paperwork needed to buy and possess ammo. Canadians run into the same sort of issue crossing the border with their guns. The guys at the trap club simply bought a five dollar Minnesota nonresident small game license (but because not US citizen, they have to also complete ATF Form 6).
Incidentally, I do know the US does restrict ammo transported INTO Canada and yes from time to time they do stop vehicles leaving the country on US side and check them. The trap club crew ran into this a few years ago.
So the long answer is moving ammo across the border is almost as complicated as moving guns. A bit less so for those of us who are dual citizens ... but we are not entirely immune.