I fish the Frome for grayling as often as possible so this advice might just be useful.
I'm not sure about all stretches of the river, but the water controlled by the local clubs are open to coarse fishers from 1 Nov to the last day of Feb.
The best method, and definately the most enjoyable is trotting. I use a centrepin loaded through with 3lb line, usually to a size 16 hook.Your choice of float will depend on the swim and flow. It can alternate between a light (for a fast flowing river like the Frome) 3 or 4BB to a 4 swan chubber. The Frome is quick to react to weather and rises quickly after rain. It also gets back to fishable conditions after a couple of days without rain. I would definately agree with the earlier tip about waders and a bait bib though I've never thought about the swivel. You decide.
The most prolific bait is maggot. I usually have 2 or 3 on the hook and a red/white combination seems to be best. I've also had success with red worms or corn and these baits often sort out the bigger fish. Long trotting on some swims produces at the beginning or end of the trot for some reason, but always be prepared! Also be prepared for dace, which strangely were absent last season, and the occasional salmon. I don't get out nearly as often I wish my wife and kids would let me, but I hooked into salmon 4 times during my short sessions last season, and with the tackle described above, they certainly give a run for their money! I managed to land 2 and was dead chuffed with that.
Don't forget that the Frome is a small river so be prepared to move swims when bites stop.
I hope this helps. I think my most enjoyable fishing trips have been grayling fishing on the Frome. It is a beautiful river to fish and success or failure it's always a pleasure to be out on its banks.