If you're travelling with your family, hiring outstation cabs is a best idea. Bardhaman to Kolkata is about 105 kms via NH 19. This is the fastest route despite usual traffic and the distance should be covered in 2 hours. This road promises a beautiful scenic view along the way.
The best time to visit Kolkata is right after the monsoons, as autumn(October-November) sets in the city sets in the spirit of Durga Puja. Larger than life pandals, beautiful durga idols, various delectable dishes. If you want to soak in the actual spirit of Bengal there can be no better time. The place is a bit crowded though during the Durga Puja. The winters(December to February) in Kolkata are pleasant. This is perhaps the best time to go sightseeing in Kolkata. The Kolkata book fair is also held around this time. The summer(March to May) season is hot and humid and best avoided. The Monsoons(June to September) do bring some welcome relief from the soreing sun. However, the daily life is highly disrupted as streets are flooded during monsoon.
There is only one road route from Bardhaman to Kolkata.
The roads are excellent. With online cab booking in Bardhaman all you have to do is sit back and enjoy till you reach your destination.