For traveling to Madurai from Bangalore you've two equally popular options : Train and Road.
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.
The weekly Nagarcoil Express ( Train No : 16537) operates between Bangalore City (SBC) and Nagercoil Jn (NCJ); For the Mumbai CST to Nagarcoil Express (Train No:16339) and Vivek Express ( Train No:19567/19568 from Dwarka to Thoothukudi ) , get to Krishnarajapura railway station ; Also for the triweekly Dadar to Tirunelveli Express (T No: 11021) get to Yesvantpur Jn .
Similarly you'll also find many daily bus services (KSRTC, TNRTC and private ) between Madurai and Bangalore.
If you are planing to drive, it is a pleasurable drive on the 4-6 lane highway all the way (NH7), though you'll have to shell out toll fees at regular intervals!
Nevertheless you'll be able to cover this distance in about 6 hours or so.
Both road and rail routes go through more or less the same towns and cities.
Here is a top 12 traditional shopping places in Bangalore