Sorry but you can't change the centre once you filled for BITSAT once you have filled the form. But if you feel that your reason is way too important and centre change is the necessity then you can try contacting their academic offices and talk to them about your issue.
They will give the best answer
You cannot change the BITSAT centre once you have submitted your preferences since the link for editing the application form was available on the website from 22nd March 2019 to 25th March 2019. But if there is a serious problem and you can't manage to go to the selected/ allotted test centre, then I would urge you to drop a mail at email@example.com giving valid reasons. They may change the date/ test center if there is a clash with some other competitive exam/ board exam. Though there are slim chances that they will entertain such email queries in this regard but trying doesn't hurt.
Hope this helps.
as per the official website of bitsat there is no notification yet regarding the change of centres but please stay tuned as they allowed the change of centres in case they had a clash with some other exam and the exam was conducted at a later date for them at the new centres.
hope it helps.