If a person was convicted and sentenced to ADC and they are waiting in county jail till ADC has a bed available can they get an ADC bond? How would we get one? Who do we call? How much is it?

ADC? Arkansas Department of Corrections?

ADC? Arkansas Department of Corrections?

Yes Arkansas department of corrections

Contact a bondsman or the prisoner's attorney.

If they are sentenced to Prison, you can not "bond" out. They are serving their prison time currently at the local jail, till there is space at the regular prison.

OP will no doubt get credit for time served in county jail.

As noted, generally, there are two types of release bond: pre-trial, and pending appeal. If neither apply, I don't think OP qualifies.