Do you know the names of the varieties and the rootstocks? I always start my bare root plants in pots, in good quality potting soil, and have around five apricots growing in pots right now.
First, look at the size of the roots, the way they grow, and get a pot which would allow the roots to spread out and down as much as possible. A fifteen gallon plastic pot half filled with soil seems to be better for the plants than trying to cram the roots into a five gallon pot. The larger pots don't dry out as fast as smaller ones, and in our hot summer climates, keeping the pots watered can be a challenge. After a year of so, if the roots start growing out of the holes on the bottom, it's easy just to lift out the root ball in a 15 gallon pot, add 6-12 inches of fresh potting soil on the bottom, two teaspoons of slow release Osmacote fertilizer mixed in, and replace the tree at the top. And it saves buying another pot.
You plant the trees in pots the same way you would plant them in the ground, spreading the roots out to their natural level of growth, filling in the potting soil carefully so the roots aren't compacted together. The branches are pruned (or not) to balance the root spread. If the roots are long and ample, the branches need less pruning. If there are a number of long branches that make the tree top heavy, then they can be pruned back by half.
The article below will give you more information. Good luck.

Here is a link that might be useful: Fruit Trees in Containers

Thank you so much for the info, altadenamara! It's good to hear that someone else has successfully grown apricots in pots.

Since you asked, the apricots are Moorparks, which apparently grow well in this area. I don't know what the rootstocks are, but I do know that they are not dwarfs.

Question: if I want to keep the trees rather short (6 ft or so) do you know if I should prune it now or wait? The trees are currently about 5 ft tall with just one long central "trunk" piece and a tiny branch or two at the top that forms a "V" with the trunk.
Thanks again for your help.

In a pot you should prune them back to about 18 inches. This should be about 12 inches above the graft union. You want the branches low and at near 90 degree angle to the trunk. Pruning hard and low will get you the strongest branches and a low tree. That's how I did the ones I just planted in 15 gal pots.

The Fruitnut

Thank you, Fruitnut, for taking the time to respond to my query. I will do as you suggested.