Stiffen Floor with bridging between open web floor Trusses?
No, do not add bridging between open web floor trusses. @Jasen is exactly correct.
Bridging, blocking, etc. does not add much strength for bending anyway. It would be better to add a bearing wall or reduce the span if possible. However, you can’t just add a bearing wall without having the manufacturer verify where it will need to be installed. Then, of course , you’ll need a footing, etc.
Open web trusses are designed so that the top chord is in compression ONLY, the bottom chord is in tension ONLY and the diagonal chords are either in tension or compression ONLY.
When additional blocking, bridging, etc. is added, it allows forces to be transferred from truss to truss. This action is called “double bending”. That is to say one of the chords could be in tension and the additional bridging could cause the chord to be in bending...tension and compression. That additional tension could exceed the allowable stress of the member or the connector.
You have open web trusses not I-joists, but the effect is similar. The additional bridging, etc. could transfer additional loads that exceed the web strength, chord strength, or the glue strength between the web and chords.
You’ll need to consult the truss manufacturer to see where additional bridging, etc. can be added. (I doubt a structural engineer will assist you because they didn’t design the connectors. )