I can't think of a specific plant that would meet your requirement, but consider this from a gardening perspective - the reason why we use annuals in the garden is because they flower the whole season. Perennials - generally, there are a few exceptions - only flower for a short period of the spring, summer or fall.
Forget-me-nots are just one such exception - they will flower prolifically from spring til fall. They will get very full, but the flowers aren't big and showy like petunias. They do a great job filtering though and if you wanted only one plant in your bog, they would work.
Did you know you CAN plant impatiens in water? They prefer more of the marginal edges - not fully in the water, but wet feet are fine. So you could add a few to the edges of your bog to give you some all season color and then plant one or two other things in the middle to give you that planter look.
Share a few pictures of your bog so we can see what you're working with!
Here's a few photos for an idea of how these work in water. This is my pondless water fall with forget-me-nots. I took this one because I rarely get flowers on my floating hyacinths - so don't be distracted by that lovely flower! The forget-me-nots are in front of the leaping frogs!
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And here's impatiens growing in my waterfall - these are planted where they are wet all the time - they do AMAZING:
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