Decide if the song needs a bridge to begin with. Don't force it. If your song has an intro, verse, pre-chorus, chorus and solo, a bridge may be overkill. Consider what parts you wish to connect. The length of the bridge should be relative to the whole of the song.
Present a new lyrical idea in the bridge. For example, if the verse of a song talks about a lover leaving and the chorus describes the heartbreak felt over it, the bridge might be about doing fun things to cure this heartbreak. Good bridges often take the storytelling elements of the verse and the emotional response of the chorus and elaborate on them in a call-and-response fashion. For example, in one line describe a fight with a lover and in the next, talk about how sad it made the other person feel.
Introduce new chords or switch from major to minor chords to take the song in a sharp, new direction. If verse and chorus progressions are generally faster, try slowing down the bridge, or vice versa. Experiment with new rhythms in your bridge. The chorus melody of the song should usually be higher in pitch than your verse, and the bridge should build in pitch and energy as well. The chorus usually follows the bridge, and you want to make a dramatic entrance into it to stress its importance.
Make sure the bridge transitions well from one part to another. It should present a twist, but not sound so out there as to be awkward or clash with the main key and chords of the song. Many songwriters have a collection of bridges stored up to use when they need one, but make sure they actually fit before putting them in a song. Consider the parts before and after the bridge so the transition is smooth. The bridge is often a good place to raise the key of a song, but be sure to maintain this key change going into the next part of the song.
Consider the placement of the bridge in terms of the overall energy of the song. A bridge might sound better right before an instrumental rather than before the last chorus. Try different combinations. Although unusual, try placing lyrical or melodic hints to the bridge in different parts of the song. In Fall Out Boy's "Dance, Dance," the bridge melody and lyric appears at the end of the second verse. In AABA, an older songwriting form lacking a true chorus, the bridge, or B section, usually occurs once or more in the song, whereas the main A section appears more often.