Only system that I know of that could work that way would be a deionization filter. Unfortunately they tend to get used up quickly if you have even moderately hard water. Reverse osmosis will produce more water for a longer period of time but will require a good amount of planning and plumbing to set up an automated system.

Chris,
You should have no problem setting up a reverse/osmosis system. It is easy and well within your needs. The only considerations you need to be concerned about it the life of the filteration membrane and that of the filter cartridges too.
I use a SpectraPure system that I put in myself. I do not have it dripping into a bog but into a rain barrel where I can drain it off into jugs for hand watering. You do not even need to do that. All you would need to do is to have the drip line that the r/o water comes out of feed into a hose, even a garden hose, and arrange the flow to conform to gravity feeding of the bog. Just run the system 24/7.
To use gravity feed you only have to hang the system up above the faucet that feeds water into the r/o system.
So all you would have to deal with is the gradient from the outtake of the system to the intake of your bog feedline.
I am including the link for SpectraPure. I'm not connected to it in anyway apart from being a very satisfied customer.

Here is a link that might be useful: SpecturaPure