Hello Suzan, i cannot say if aims mandya has a bus service or not since it is not mentioned in the website, but i am sure that like any other institution it would have a transportation system, or atleast public transport at the disposal of students for travelling to and fro the campus. It should be safe for girl students because like you there would be many other female students taking this service of either public or institute system. but given the distance between aims mandya and mysore, i doubt that there wont be any institute bus going that distance and you have to rely on public system. 

Mandya to Mysore is 46.4 kms and that would take 56 mins. however aims mandya to mysore is 87.3 km (1 hr 56 min) 

The campus of aims is fully residential with hostels available for all students