Does someone who has poa have the right to bail people out of jail?

You cannot bail yourself out with the principle's money.

Is the person getting bailed out of jail the person the have POA for?

Just about anyone can bail out anyone. What is the rest of the story?

Who does the POA want to bail out?

I would think that they would be responsible for using the principal's money to bail out the principal.

If the principal may need Medicaid in the next 5 years, the POA should not use the principal's money to make a gift of bail money to anyone. An interest free loan is also a bad idea.