It looks like you're in the key of F (I), playing a II7, V, and iii so far. Maybe go to Bb (IV) for the bridge? Incorporate a Dm (vi) somehow?
A useful formula that may be helpful are the chords that are diatonic a particular key are defined as:
I, ii, iii, IV, V, vi, viidim
It's not a hard and fast rule, but it may be a good start to hunting and pecking for a bridge.
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