I had a court date on Tuesday in one county but got arrested in another county so I missed the court date because I was incarcerated. So my question is with a letter of incarceration when I get realease to the county that I missed court with will I have to bond out sense I have a letter of incarceration

I am sure you notified that court that you were in jail, and were not going to be there ? And depending on the charge, most likely there is a warrant out for you now.

And honestly the other court does not care why, just that you were not there, ( a few judges would accept a good reason) but to say you were not there because you committed another crime my not be your best defense to a judge. ( against depending on the offenses)