I think the GB Express (out of Simpson Bay) is smoother but about 3X (or more) the cost of the public ferry. The public ferries are all different but all take about 20 minutes. Of that 20 minutes, there is perhaps 6-8 minutes of the crossing that (at times) gets a little bouncy. If you can get on a ferry that has an open top deck, that eliminates some foe the potential for seasickness.

You can fly to Anguilla also but the public ferry is a good and inexpensive alternative.

Here is a link. Might be a little dated but it will give you a basic idea of cost and schedules.