Can Surety in a Cr Case travel abroad?

the surety can travel abroad.  There is no bar normally.  But if the person (accused) absconded or not appearing for courts several hearings and failing to appear when direction issued by court law, the action will be taken against the surety for the amount to which bond has been executed. 

No need to take any permission from Trial Court for surety to travel abroad.

I don't think so that any person who is having any criminal record in the police station can travel the abroad. First of all, that person would never be allowed to visit such places due to this criminal record. Also, these people should not be allowed to have the tour of those countries too. I prefer to check travel finance sites to manage financially work. On the other hand, if they are up to abroad visit then there must be a proper procedure for them to let them go because without that it is always a risk to let them go.

well advised