Crossing the Memorial Bridge from West Springfield to Springfield can be intimidating for a cyclist who is not accustomed to riding assertively and can be confusing for a cyclist who is not familiar with the neighborhood. However, with the proper skills, it is easy and nothing to be afraid of. However, there are two tricky elements that you should know about.
The first tricky element is the rotary at the west end of the bridge. This rotary consists of a single very wide lane. Staying too close to the outside will result in motorists failing to yield to you when they enter (drive-out) or exit (right hook) the rotary, but staying too far from the outside will make it difficult to exit the rotary, since you will have to yield to traffic passing you on the right. I find that the best position is far enough from the center island to enable motorists to pass on the left, but no farther, so that other drivers exiting the rotary will not be tempted pass on the left and cut in front of you. This is approximately the middle of the lane, but it is not a lane control position because the lane is so wide.
The second tricky element is West Columbus Avenue, at the east end of the bridge, It is a southbound one-way street that runs along the river, and it has an erratic lane configuration. It provides the fastest route from the bridge to State Street. When you turn right onto West Columbus Avenue from the Memorial Bridge, you will see three lanes. If you are a timid cyclist, you might be tempted to stay in the right lane, but then you will have to change lanes later when you want to turn left. If you are a confident cyclist but unfamiliar with this street, you might be tempted to move immediately into the left lane. However, the left lane goes into the parking garage, so the middle lane is the correct one to use if you want to turn onto State Street. After the entrance to the parking garage, this lane widens. Also the right lane splits into two. You might again be tempted to keep left in preparation for a left turn. However, the left side of what is now the left lane turns onto the I-91 northbound entrance ramp. So you must keep to the right of what is now the left. After the ramp, this lane become the left-turn lane for State Street. So you are exactly where you wanted to be, and you never had to do any side-to-side maneuvering.