how to make a bridge
 

When writing a chord sequence for song, and you feel that it needs a bridge, is there a formula that can be used to decide on appropriate chords?

As an example: I have a song that is based around Fmaj7 and Cmaj7 for the verses and then goes to F G7 C F, F G7 C Am for the chorus. I really feel that this tune could be better with a four bar bridge. What chords could I use? and is there some kind of formula that can be used to make a bridge in any particular key?
I hope all of that makes sense. What I suppose I am asking is how to connect a verse to a chorus using a bridge. I know that there are no hard and fast rules, but is there some kind of guideline at all?
I am not very clever with theory, so at present I just kind of fumble around until something sounds O.K. I need to have a way of speeding up the process.

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.

I don't know what will work for your song, but in my own writing bridges most commonly start on the IV, V, or ii ....but there is no rule or formula. You do what sounds right.