My doctor has suggested that I have a spine fusion in my lower spine. How will this affect my ability to bend over?

This is dependent on. How in shape and how flexible you are in the first place as well as not having any hip or leg issues at the same time. The type and extent of your surgery plays a role as well as the diagnosis for which you are having the surgery for in the first place. For most, there is usually not a noticeable change once recovered from the surgery.
Depends. A patient's residual lumbar motion after fusion depends on the number of levels fused. Most of a patient's functional bending happens through the hip joints. The lumbar spine is responsible for the majority of twisting and this will be limited proportionally to the number of levels fused.