You can get one of the many buses to Pondicherry at the main bus station at Koyambedu. Most of these buses are quite inexpensive and offer very basic facilities and lack both air-conditioning and comfortable seating. The buses get rather packed with a lot more people than are supposed to be permitted on board and is definitely not the recommended choice. The journey takes between three and four hours, depending upon what kind of bus you take.
The preferred road from Chennai to Pondicherry is the East Coast Road (commonly knows as ECR). This is a very scenic highway, with sand dunes on one side of the road and the sea on the other. The journey takes about two to three hours. Midway you cross Mahabalipuram which has a number of temples you could visit. There are also a few resorts where you can stop to dine. This route passes through Mahabalipuram, Kalpakkam, Marakkanam, and Kalapet before reaching Pondicherry.
The other road to Pondicherry is the National Highway 45 (NH-45), also known as the Grand Southern Trunk or the GST Road. Taking this road will take you about 3.5 hours to reach Pondy. This road is less scenic but a lot safer than the ECR as it has a divider between both sides of the road for much of the way. This road passes through Tambaram, Chengelpet, Madhurantakam, Melmaruvathur, and Tindivanam before reaching Pondicherry.
Many taxi services are available on this route. Taking a taxi from Pondicherry works out a lot cheaper than hiring one from Chennai. However, as you have to pay for a return trip for the taxi this might not always be true. Make sure that your driver drives within the speed limit of 60-80 kms/hour.
For the folk who want to drive down, both of these roads offer a great experience. There isn't too much traffic, the roads are of good quality. You just have to make sure you don't get too excited and hit the accelerator. Drive with caution, especially on the ECR, as a number of accidents have occurred on that road.
There are many bus options to go to Pondicherry from Bangalore. Government services as well private bus services, luxury buses as well as less luxurious "deluxe" buses. The journey takes between seven and eight hours. The preferred buses are the ones that do an overnight journey. However, beware that tickets, especially for weekends, are pretty hard to come by. So make sure you book well in advance.
You can board most private buses either at Kalasipalya or at Madiwala. Government bus services start from the Kempe Gowda Bus Station. Most overnight buses start at around 9 or 10 PM and reach Pondicherry at around five the next morning.
Some bus services I have travelled by extensively with a reasonably good experience are Indira Travels, SRS Travels, KSRTC, and PRTC. KSRTC and PRTC both have semi-sleeper Volvo buses, which are a bit safer and a lot more comfortable than other buses.
The road to Pondicherry from Bangalore is of about 350 kms. Take the Hosur Road till Krishnagiri, take a left off the main highway (road signs show the turn) and then take National Highway 66 (NH-66) to Thiruvannamalai and then to Pondicherry. You will cross Uthangarai, Chengam, Tiruvannamalai, Gingee and Tindivanam on the way. The journey takes between five and six hours. Gingee has a fort which is a great place to take a break. Make sure you pack some food as there aren't any good places to dine on the way.