The only way for you to visit Goa from Bangalore over a weekend is to fly in and fly out. A distance of over 560 KM is far from being an ideal weekend getaway - if you are travelling by road or train. It would take no less than 14-16 hours to reach Goa from Bangalore by bus. Trains would be no different. So excluding the travel time, you will be left with just 24-36 hours to explore such a buzzling destination, which is not justifiable at all.
Bangalore to Goa Flights: There are multiple direct flights between Bangalore and Goa. Low-cost carriers like Air Asia and Go Air also operate in this route, so you can possibly get it cheap - if booked 1-2 weeks in advance. I just checked the Bangalore-Goa air ticket fares on MMT, and it can cost you a little over INR 3000 for one-way flight ticket. If that's within your budget, then you can go for it.
If you prefer to travel by roadways or railways, then you should atleast have 5 days (including the travel time) to explore Goa in a good way.
Bangalore to Goa Buses: There are overnight buses that run from Bangalore to Goa on a daily basis. The roads are in great condition, so the bus journey will not be too hectic. Both AC and Non-AC buses are there for you to choose between. Volvo, Mercedes and sleeper coaches are also available. A semi-sleeper non-AC bus would cost you around INR 800, while a AC Volvo ticket comes at around INR 1200. SRS Travels, Paolo Travels, Seabird Tourists are some of the renowned bus operators that connect Bangalore to Goa on a daily basis.
Bangalore to Goa Trains: As far as the trains from Bangalore to Goa are concerned, the Kacheguda Yesvantpur Express (Train No 17603) runs daily between Bangalore and Vasco. Besides you have Vellankanni-Vasco Express (Train No 07316) and Chennai Centrail-Vasco Express (Train No 17311) running once per week. Both these trains have scheduled stops in Yesvantpur railway station in Bangalore. Moreover, there is a direct train between Yesvantpur and Vasco (Train No 17309) which runs on every Monday and Saturday. It takes around 14 hours for the train journey between Bangalore and Goa.
So there are quite a few options to reach Goa from Bangalore by train, but you need to book well in advance as these trains run to their full capacity almost always. You can probably try your luck with IRCTC Tatkal ticket booking.
Regards,
Deb