hello,

yes, you can definately persue your ME career in CSE from any of the BITS campuses. In order to do that you can give either GATE exam or BITS Pilani conducts its own exams for higher degree progam named "Higher Degree (HD) Programmes". For appearing in the exam you should start preparing for your CSE subjects in order to give the exams. From HD Programmes you only get BITS campuses but if you qualifies GATE you are eligible to apply for as many institutions you can which includes IIT, IIIT, NIT, CFT, all other private colleges including BITS.

hope this will help you

all the best!!