The easiest wat to reach Mangalore from Bangalore would be by taking the train from Bangalore. There are two trains running in the route. Kannur exp starts in the night and will get you to Mangalore by morning.
There are volvo and luxury buses plying between Bangalore and Mangalore and if you are using public transport then bus is ideal as it is far more frequent.
It is better to avoid traveling by car.
The distance between Bangalore and Tannirbhavi just 12 kms from Mangalore is approximately 350 Kms. There are two trains running in the route from Bangalore and many buses plying between the two major cities.