I don't thik that You did anything wrong. I have similar experienc.
But after pinching the soots with flower buds I got some more growth until the weather got warm. I think they are meant to be picked young once, just like lettuce not like basils.
But I like their peppery taste and zest. I had two differnt kinds. One with wide, multi-lobed leaves and white flowers and the other one with narrow oval leaves and yellow flowers. I let one of each to bolt and make seeds. Now they Are maturing their seeds. I will plant them late summer as fall crop from my own seeds.

Ahh i thought they were just like basil and woudl produce leaves through the year. I guess the best option then is just to replant the seeds it gives you throughout growing season right?

You've got it ncage.
Arugula is a cold crop just like lettuce. In zone 5 you should stil have more time to enjoy them.
Let one bolt and let just one branch or two gor for seed. pinch the rest of flowerin branches. Whole plant can make a ton of seeds. Support the seed branches and let it matue. Pull up the plant before the seed pods get dry (and may explode open) Hang them Upside down to fully dry and mture. You can put a brown bag over the bunch, held by a not-so-strong rubber band so the seeds wont fall off all over the place.
I Don't know this will happen , but it is just a precationary masure.

I always save some seed but next year I'm building a 4x4x3 ft box type planter just for Arugula and will let it self seed. FUNNY, THE FIRST TIME I tasted this plant; I could not stand the taste and now I crave it.

Think of it by its other name (more common outside America) - Rocket. Like coriander (cilantro), it takes off with great speed, and like fireworks rockets, it fizzles out quickly, too!

In my subtropical part of the world, it's a winter-only plant. It will bolt to seed in the heat. In fact, in will bolt to seed with any marked change in temperature, too, like a sudden cold snap or an unusually hot day.

As with coriander, successive sowings/plantings (perhaps every 2 weeks) is the only answer. Let it self-seed, and in theory you should have a perpetual supply - eventually.

Meantime, you can't change the nature of the beast!