Nothing to worry about that it may happens with many students that they mess up their paper even if they have prepared very well for mains. JEE is not the only option to get admission into good colleges for engineering talking about bitsat, the paper is usually easy than jee mains but the paper is a bit lengthy so you need to do some time management and do some model papers and last years paper before the exam and as you told that you've studied well for mains I don't think then you need to worry much about bitsat because the topics covered in both exams are kind of same so go for a revision polish your concepts and practice well and you are good to go. 

All The Best!!.