Hi, Some of the best and top management institutes in India for IB are:
1. IIFT
2. MDI Gurgaon
3. KJ Somaiya
4. Symbiosis Institute of International Business.
5. Fortune Institute of International Business
6. GITAM Institute of Foreign Trade.

Most of the colleges take through management entrances like CAT, CMAT, XAT, SNAP etc..

The applications have started for CAT and XAT.

Check the notification for various management exams here.
Good Luck.