One is a Pinus mugo 'Valley Cushion' and the other Pinus mugo 'White Bud.'
The plants are in their nursery containers.
My questions are; can I at this time of year repot these into bonsai pots?

NO! From my experience, these miniature mugo pines are extremely sensitive. You
can style them now, but only repot them in early spring.

Is there anything that I need to look out for in repotting them?
Can I bareroot them now to get them into a good bonsai soil mix?

Never bareroot a pine. You can gently shake off the excess soil, but only
replace the soil around the roots gradually. After repotting, leave them in the
shade for a month.
Now somebody may say I am mistaken, but I am reporting from my experience &
what I have been taught by experts around here. (Upstate NY)

Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)