Butterfly bushes are becoming an invasive plant across the country. I'd say don't plant anything around the bush so you have easy access for cutting off the dead flowers. That way the bush does not produce seeds, plus the bush will produce more flowers for the butterflies.

Here is a link that might be useful: county level US map - where butterfly bush has become invasive

I agree. Standard butterfly bush can be 6 to 8 feet tall and you'll want to be able to get in and dead head.

Echinacea actually does pretty well in partial shade, so you can try that about four feet away.

I haven't had any issues with butterfly bush self-seeding here in Z6 but once they bloom I dead head them regularly to prolong the bloom period. I leave the last of the flowers on the plants to go to seed in late autumn. My 5 winter sown plants (i.e., grown from seed) are set in different beds around the garden and grow to nearly 6 ft. each year. Planted around them are peonies, blackberry lily, Siberian iris, Maltese cross, gaura, ornamental grass, daylily, Shasta daisy, balloon flower, gloriosa daisy, baptisia/false indigo + lots of other full sun perennials (most grown from seed via winter sowing).

From the OP's photo, it's difficult to know whether or not the corner of the fence area gets full sun (6-8 hours) which butterfly bushes need.

I wanted this bed to have a cottage garden look and as you can see, the butterfly bush (center) does fine planted among other sun-loving perennials.

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Also growing in the bed pictured above are blanket flower, coral bells, astilbe, artemesia/silver mound, Montauk daisy, dianthus, evening primrose, verbascum/mullein, spirea, Cupid's dart, iberis/candytuft & hardy geranium/cranesbill.

I love butterfly bushes! It's a little too cold here for them to do really well, but in protected areas, they're beautiful. I plant coneflowers with mine, which look amazing, together. Also nice with roses, bee balm, daisies, cosmos, in fact, lots of flowers.

The yellow jackets completely mellow out, on butterfly bushes. Plant some in the back of the garden (out of the path) and the yellow jackets almost act happy/drunk, on them. Of course, butterflies like them, too...and they keep deer out of the garden, especially when planted in the back or sides! One of my favorite shrubs :)

Washington is the state where butterfly bushes are causing the most problems. It is classified as a class B noxious weed by the state.

Here is a link that might be useful: King County, Washington noxious weeds - butterfly bush