I have a bog garden here in North Carolina, fed by a fish pond (see pic below from when I just installed it). While I used plastic liner for mine, the principle is pretty much the same as using a tub so I feel comfortable weighing in here. I had to poke a few small drainage holes in the bottom of the liner so it didn't get totally swampy, and I mixed a good amount of beach sand in with the pure peat moss (about 70/30 peat/sand ratio). From the research I did, this seems to mimic their natural habitat most closely. I have to say that after 4 years, the four sarracenia I planted are all doing fantastically, and have tripled in size. Many of my sundews also come back year after year, and I even have Venus flytraps survive my 7B winter (one grows massive 2" long traps now!).

The two things I have that you might not are a deeper hole--about 24"--and consistent moisture from the overflow of my fish pond after each rain. So my pitchers have room to really entrench their roots, and stay consistently moist while still getting full sun all summer. This was all part of my deliberate design, which worked out better than I even hoped for. For what you're doing, the depth might not be a huge issue for purpurea. But the consistent moisture will be...unless you want to be watering that tub every other day you may find toasted pitchers. Consider an automatic watering system from a rain barrel, or using a drainage system to divert water into the bog garden. Also remember the soil needs NO nutrients...just peat and sand (no gravel or anything else that might add calcium or other nutrients). The pitchers will get their food not from fertilizer or their roots, but from the insects they consume. Take the time now to set up the moisture and soil correctly, and it will be a wonderfully carefree carnivorous corner in your garden!

My pond and bog garden after initial installation...the pitchers are now triple in size and I'll need to divide soon!

With that container type of bog (even large containers such as the plastic tub), you could achieve some level of constant wetness by having drain holes a few inches above the bottom. That way, there is a kind of reservoir that will collect rain/distilled water, and the water will drain out upon reaching that drain hole, so the pond does not become flooded and lead to other problems.

The wicking nature of your medium will then draw the water up to the higher parts of the tub, where your plants can use the water.

Keep in mind that a bigger tub may look more dry on the surface but hopefully you have a good moist condition 1" or below the surface for the plants. The idea on this is that even in 1 growing season, a newly purchased or propagated CP may have roots that are 4 or more inches, so the top looking dry is not as detrimental to the plant.

The idea of having water overflow into the bog container from another source is a great idea, so that you don't have to mind the watering as much. However, if you are diligent about keeping it moist, even in times of low rainfall, your plants should be OK.

As for the part about your natural soil seeping into the bog via the drain holes, I think that it's about concentration of the contaminants. For example, we may accidentally spray hose water in the general direction of the bog. It doesn't mean the plants will immediately freak out and die. We may use distilled water with 0 or 10 ppm. From the water point-of-view, that is different but for the CPs, they can handle various levels up to about 50 ppm.

In the same way, small amounts of soil falling into the small spaces between the peat material will not negatively affect the plants. It could also be that the drain holes would be much deeper in the tub than the roots will ever get to.

I use a kids pool with a hole drilled in it about 2 inches from the bottom and put my sarrs in pots filled with moss and ether sand or I prefer pumice and I keep it filled to the hole If it rains the extra drains out , sarrs are native to new jersey so you should have no problems growing them