First, have you determined how many beaver you need to remove? You need to know if it is old damage they are complaining about with nothing present to catch, a single beaver, a pair, or family unit before starting anything. This not only can help you choose sets and locations, but it can also help you from making mistakes and educating any survivors.
Second, if beaver are present make sure you find the den or hut stay and if a family group is present, stay away from it. I've had jobs (at this time of year) where there was an old hut that the beaver would only occasionally visit while they lived in a bank den on the opposite side. With the equipment you've listed, I'd try the bodygripping traps first then move to the Bridgers if necessary. Personally, I'm terrible with bodygripping traps and am spoiled since I can use snares and now the Comstock and Advanced Trap cage traps but I'd say use the bodygripping traps in the following "snare" sets. If they aren't productive, you can always move to the footholds.
I prefer to use a food lure at this time of year, so first I'd look for a good tree that has water all around it and preferably limited access on both sides. You can always "restrict" the distance by moving materials to help fence it down, but I like to have as much natural fencing in place before I add anything to it. Next, set two bodygripping traps, one on either side of the tree and have them on 10 feet of wire/cable anchored to the spring furthest away from the tree with and also anchored to a tree with one upstream and one downstream. This allows a trapped beaver to move away from the set so it cannot be seen by others. I'll state that this doesn't always work, but I'd rather have the capability for it to work than not. Lastly, take the food lure and smear it on the tree about 3 - 4 feet above the water line. This will have the beaver swimming around the tree looking for the scent. If you have to have the 330s fully submerged underwater, use dive sticks on top. If this isn't a requirement, you can leave 1/2 in and 1/2 out with triggers on the bottom. The key is to limit travel around the tree to the space the 330s are sitting in. Again, you don't want to put too much fencing in as it is better for the beaver to be able to swim in slowly constricting circles around the tree and get caught then to scare them away because you built a 20 ft fence on each side of the tree that wasn't there before.
Another set you can do that is similar is to use 2 floating logs to make a channel with the 330s on each end and dive sticks above them. I've done this once before with the logs being about 18 - 20 inches in diameter and about 10 ft long. There was a small tree growing between them that I put the lure on and was able to push the one log closer to narrow the channel to bodygripping size then stake it in place and put some extra limbs over top to try and prevent the beaver from swimming on top of the new channel. I had a snare on one end and a 330 on the other and ended up with the beaver in the 330.
A set I do with 330s is to break a small hole in the dam at the edge so I have enough water running through to make some noise. I then install a 330 about 6 feet from the break in enough water so it has several inches over top of it (with the break, it can become exposed quickly if too much water is running out) and put fencing in on both sides with the majority of it being coming from the bank. I've never had the 330 pulled and used to repair the dam and would rate it at about 70% successful under the right conditions.
If you need to use the footholds, consider making a castor mound set away from the bank on a log. When I do this set, I always try for a front foot catch and use two logs on either side like a "V" to help guide the beaver into it. When setting for a hind foot catch, I always do so on pullouts and shave away the bank and then make the trap bed so the trap is setting about 16-18 inches below water with a vertical wall behind it. Remember to offset your footholds about 8 inches as the feet are off to the side and not underneath.
When using the Comstock or Advanced Trap beaver traps, I look for choke points with the runs and just set the cage traps in the choke points, make sure no sticks are in the way to hinder door closings and walk away. I don't know about others, but I can say that I can place a cage trap in 1/2 the time or faster than it takes me to do any other method.
