If you are taking public transport, your best option is getting into the rare buses (5C, 5K, 5T and 23K) that actually come into CIT campus and stop outside the Women's Polytechnic, or WPT (2 minutes walk from IMSc).
Your next best bet is a bus coming to Indira Nagar water tank (6D and 21D), just across the canal from WPT (5 minutes walk from IMSc). These buses are rare too.
In practice, you are most likely to get a bus upto Adyar Depot (10 minutes walk from IMSc) or to Madhya Kailash (a good 1.5 km away from IMSc).
Note: Adyar Depot is an entity distinct from Adyar signal or Adyar Bus Stand!
There is a good bus A1 which takes you from the Central railway station to Adyar bus depot (and beyond to Tiruvanmiyur). It has certain fixed plying times, but will have extra space for luggage, cushioned seats etc. It costs Rs. 11 inclusive of luggage from Central to Adyar Bus Depot (see below). The earliest 1 cut bus to Central starts from the Depot at 4:45 a.m. After which there are buses to Central at 5:15 a.m., 6:30 a.m. going on until 8:45 p.m. The buses from Central are 30-45 minutes after these times.
If you are feeling adventurous, you could take other buses from the station. Cross the Poonamallee High Road in front of the station and get to a long bus stop with several sections. Several buses (6A, 4C, 4) from here will get you to Adyar Bus Depot, from where the Institute is a 10-minutes-walk away. To find your way from the Depot, use the local map. If you are very lucky, you may even get a 5C bus all the way to the Women's Polytechnic bus stop. From here IMSc is just three buildings down the road.