Can I do BE from a reputed college in Bangalore after doing Polytechnic in EE in Pune?

Somesh, yes you can do it subject to fulfillment of eligibility criteria. You have to appear for Lateral Entry Engineering Test (LEET) for admission to BE/ B.Tech lateral. You must have min.of 60% marks in diploma to appear for LEET. If you have not given LEET too, then opt for good private univers