Take the overnight Tuticorin Express or take your car for a 9 hours drive!
This highway can take you to Kerala and Tamilnadu from Bangalore city.
The Tuticorin Express (Train No: 16235 & 16236) operated daily. Leaves Bangalore City in the night (9.20pm) and reaches Madurai in in the morning (7.20am). This is a very popular train in this sector (Mysore to Tuticorin), means check out reservation availability and book well in advance ! There are also a few other weekly and biweekly trains give connectivity from Bangalore to Madurai.
Similarly you'll also find many daily bus services (KSRTC, TNRTC and private operators ) between Madurai and Bangalore.
[#car]If you are planning to drive, it is a pleasurable drive on the 4-6 lane highway all the way (NH44). It's toll highway all the way. The route is via Hosur, krishnagiri, Salem and Dindigul You'll be able to cover this 440km distance in about 8 to 9 hours.
Overall train is the most convenient, go for car option , if you are planning to cover other destinations ( like Munnar, Palani, Tiruchi etc)
IndiGo operated direct flight to Madurai from Bangalore.