Yesterday, during a beginners class, I took a pre-bonsai and potted him into a bonsai pot. I took off less than 1/3 of the roots and potted under the guidance of the instructor. It was 80 degrees in the greenhouse. I did not want to stress the tree anymore yesterday due to the heat and potting. He needs a good pruning still. How long should I wait?

I'd wait until you see good new growth.

Even though it needs it now?

Lynda wrote:

It was 80 degrees in the greenhouse.

Lynda, 55 degrees is the temperature of a sauna.
80 degrees means you and the tree and the instructor are all dead by now.
If you mean 30°C, then it's normal for an Elm in late spring, no worries. I would have lightly trimmed it right after repotting.

I am in the USA in New England. We don’t use Celsius, so it was 80F

Lynda wrote:

I am in the USA in New England. We don’t use Celsius, so it was 80F

Lynda, I don't want to be fussy about it at all. But the rest of us not north Americans use the Metric System and Celsius, and as this forum is international based in Europe, we all get a little confused by Fahrenheits and Square Footage...
Sorry!
You can trim it when it starts to grow again as Auk has said.

I will remember that for the future. Thank you

from the pictrures I disagree with your assessment that your plant needs trimming. I would let it grow bushy first. Growth is needed for health. SO let you rplants grow big and strong, then trim.