I have a bondsmen that is certain that terms of court also applies to county court. From what I understand, the terms of court apply only to district courts. Is he correct?

County Courts shall have at least 4 terms of court annually as set by the leg. or the county commissioners. If not set, then the first Mondays in February, May, August and November. Const. Art. 5 Sec. 29.
There may be a different rule for Courts at Law. I suspect the bondsman is trying to invoke exoneration under Art. 22.13 and is likely entitled to relief.

Agreed, John.