Good LED grow lights would be the best. You should expect to need a few tens of thousands of lumens per square meter.
I understand you want to grow CPs, but can you please give an idea of specifically what you want to put in it? (e.g. temperate sundews, venus fly traps, Sarracenia rubra). Different species have different lighting requirements, and some may not even like a bog garden. For example, Nepenthes would very quickly die in a bog garden, but something like Sarracenia purpurea would thrive.