In my bag, it says how many items I have out of 350. But currently it says
ITEMS 351 / 350
which is a bit odd, and seemed to suggest that 350 is not actually the limit. So I looked it up and Niantic's official support page says
Your Bag can hold an inventory of 500 items. You will not be able to gather new items from PokéStops when your Bag is over the 500 item limit.
So what is it? 350? 500? 350 plus some buffer amount?