I purchased a 13 year old one level home with an unfinished basement. The floor joists are 2 X 10 and span a distant of about 15 1/2 feet. There is no bridging between the joists. The joists rest on the foundation at one end and on a steel I beam at the other end. The floor is level and the joist are level (they are 95 1/2 inches off the floor at each end and the same in the middle).
I have read that the best method to solve the springy floor problem is to sister another 2 X 10 to the existing joist and glue and nail or screw them together. Also, the sister does not need to run the length of the existing joist but can be either 8 or 10 foot and fastened along the middle length of the existing joist. Also, I should add bridging between the joists.