I was just getting ready to post that I'd started my slips too early (mid february) and have to figure out some way to pot them until planting time...here it is still a few weeks off. I don't want them sitting in water to root for that long.
I've always laid them lengthwise in water (halfway up the sw. potato) in my odds and ends of old crockery with good success. For some reason this year I also did some in wide mouth quarts with toothpicks and they are sprouting about the same as the others but only from one end, of course.
I've never worried about which end was up...usually my potatoes from last years crop start sprouting from one end or the other and that's when I get them out to start slips.
This year was early though, I think because our house is warmer and the sweet potatoes in storage began to sprout too soon.
I think six weeks is about right. I am pretty sure that rooting the slips doesn't take more than a week or so...much quicker than growing out the sprout itself.
Do you know what variety you have? Mine are a cut leaf kind that was given to me more than 15 years ago. I keep thinking they will play out and not produce as good but so far they have made wonderful large roots...and delicious
EDIT to add....there might be something helpful in my sweet potato thread
here
good luck!