It wasn't an issue with the ball ends protruding, just that the string hole size was too small for the actual B string to go through smoothly. I did go for a heavier gauge of strings than I would normally have chosen, as I'd read in several places that the low B needed to be above a certain size to work well. I can't remember what gauge first got fitted as it was several years ago now but probably 45-135, they were an expensive set of player-named DR strings (maybe Marcus Miller?). They were then replaced by a set of Peavey Cirrus strings (which I was sure would fit as they were designed for the bass!) but had the same issue. I think the biggest problem was where the silk windings went round the ends of the strings - I had to get a knife and cut the silk away as it wouldn't fit through at all without doing that!
Looking at some Schaller 5-string bridge drawings, I see that their string hole diameter is 4.6mm on a top-mount bridge (with a 6mm diameter string ferrule indent) and 4.8mm on a string-through bridge. As a 0.135" string has a diameter of 3.43mm (plus manufacturing tolerances), there shouldn't be an issue (although there is no indication of diameter at the start of the silk windings)
But I'm also a bit limited to the choice of bridges as I think the Peavey has a wider than normal (or wider than Fender at least) string spacing. It's difficult to find details like the hole sizes in string ferrules and bridges from most manufacturers. So I need to find an adjustable width bridge that will fit my string spacing requirements and that I know has a large enough string hole size.
Why can't it be easy?