Being a major tourist destination there are direct buses from Bangalore to Munnar however the travel time would be over 16 hours. If you travel by a private vehichle the distance can be covered in much less time as buses take much longer to commute in high ranges.
The nearest railway station from Munnar is Ernakulam. There are trains everyday connecting Bangalore to Ernakulam however its best to have own transport.
Munnar is approximately 450 kms from bangalore and the commute in itself is a vacation with beautiful views of the hills and lush greenery all around.