Cut away the drywall in the basement directly under the spot that needs support with a reciprocating saw, if you must access the floor joist through a finished basement.
Measure the distance between the two floor joists under the floor at the problem spot. Measure from one joist to a point directly across from it on the other joist.
Take a piece of dimensional lumber, such as a two-by-four, and cut it slightly shorter than the measured distance. Shorten it just enough so you can force the bridging into the span. Ensure that you use dry lumber.
Force the bridging between the joists with a hammer or mallet.
Make sure that the bridge is level with a carpenter's level.
Fasten the board to the joist using a hammer or pneumatic nail gun and 4 16d nails through the first joist and into the bridging. Toenail two nails through the bridging and into the other joist.