The 350 was imported during the 1990s, along with the 500. The 350 didn't sell.
It's as simple as that
Like the man says, they
TRIED to sell them here in the States awhile back, but there just weren't many takers, most folks simply opting for the bigger 500s for not much more. That said, used 350s do pop up from time to time
on craigslist.
Personally, though I might give a 350 a good home if it were basically given to me, I wouldn't exactly go out of my way to actively seek one out. The 500s are enough of a maintenance handful and performance compromise, and whatever the case may be in India, where 350s are by far the commonest model of Bullet, sourcing some of those special decades old 350-specific parts stateside must be like finding spares for a 1912 Hupmobile.
Up there in Alaska, I'd have thought a Himalayan might be right in its element...that, or a really well-found used or new Bullet 500 with appropriate tires for your surroundings. A '90s or earlier 350? Well, my hunch is that you could save yourself a lot of time and money by instead just sticking some old rusty iron wood stove in your shed. You could go in there and sit on it now and then, and it'll likely go every bit as fast as a 350 would up there in pretty short order, once pretty much
anything went wrong with it.