It may be too late now for the questions, but it may be helpful for others.
If you do not want to buy a "stupid" tour to travel Halong bay, you can visit by yourself, of course. From Hanoi, take the bus (or train) to Hai phong city. From Hai Phong, take the bus + boat from a transportation company named Hoang Long head to Cat Ba islands. It takes around 1.5h to get there from Hai Phong. You can enjoy the island (where you can swim and enjoy sea food) as well as you can enjoy Halong bay by a ticket to visit Halong bay from Cat Ba island. 2 days would be enough but you have still many thing to see if you stay longer.