I have not taken the bus from the airport, but it seems like a reasonable option for a team given there is enough space on the bus for people and luggage. You may have to split up depending on the size of your group.
I have ridden the Star Shuttle. This is the free bus that makes a loop around downtown Hartford.
Here is the map from CT Transit. It appears that Saturday morning may be your only issue if you plan on taking it across downtown to get to competition. Much of the time the
Fuel Cell Bus is running this route. Its a great piece of new green technology for the kids to experience.
Downtown Hartford is quite small and reasonable to walk across, but there are no guarantees as to the weather you will be walking in. The last weekend in March around here could be 60 and sunny,... or snowing.