Bucket sized is pretty small container, that will definitely limit what you can grow. Here's a few suggestions that are all native perennials, pretty hardy and easy care:
Here's some with seeds birds like, some are attractive to butterflies also. These are all full sun, to mostly sunny
Coreopsis, bright yellow, long blooming,
Echinacea (purple conflower) comes in a variety of softer pinks and lavenders and white
Black-eyed susans (rudbeckia)
Goldenrod nice fall bloomer, gorgeous with purple asters in the fall. Look for a smaller variety (some get 10' tall). It's a good one to grow in pots, other wise it takes over your garden.
Liatris (gay feather) purple flower spikes, butterflies like it.
Aquilegia (columbine) delicate flowers, don't like full sun
Butterfly weed (aka milkweed, asclepias) brilliant orange
Jewelweed (native impatiens) likes it shady
Cardinal flower (lobelia) brilliant red, likes at least part shade and moist
your Bee Balm
Maybe it's the nurseries I go to, but personally I've never found it too helpful to go to a nursery without a thought in my head about what I want. Just as I asked for a starting place, nursery people usually want some ideas about what you're looking for, before they can be real helpful.
Two things about your small containers: 1) they will dry out very fast, so you will have to be prepared to water frequently. 2) For growing perennials, they will freeze solid in the winter, it's a lot tougher on the plant roots than being in the ground. If you want your perennials to come back next year, it would help if you can protect them-- do you have a garage you can bring them in to? Otherwise pile straw or something around them... Good luck!