Just as the name would suggest, a thematic bridge is somethings that acts as a connection between two fairly different themes in a piece of music.
It would help if the two themes are connect is some way to begin with – being fragmented developments of each other, or whatever. However, it is possible to do so with very different themes.
First thing to do would be to point out where in the composition you need the thematic bridge to be – obviously between the two contrasting parts. From there look at the measures before and after it to note what are the characteristics of the opposing themes.
Finally, (and this may be the hardest part) attempt to make a “natural sounding” combination of the two themes. Be like Dr. Frankenstein and mix-n-match different characteristics of the two to form one complete idea.
Of course, this is a tip on how to create smoothness between to sections IF smoothness is desired. It is your composition – do what you want!
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