If you have multiple source files, you probably actually want to use link-time-optimization to output one bitcode file for the entire program. The other answers given will cause you to end up with a bitcode file for every source file.
Instead, you want to compile with link-time-optimization
clang -flto -c program1.c -o program1.o
clang -flto -c program2.c -o program2.o
and for the final linking step, add the argument -Wl,-plugin-opt=also-emit-llvm
clang -flto -Wl,-plugin-opt=also-emit-llvm program1.o program2.o -o program
This gives you both a compiled program and the bitcode corresponding to it (program.bc). You can then modify program.bc in any way you like, and recompile the modified program at any time by doing
clang program.bc -o program
although be aware that you need to include any necessary linker flags (for external libraries, etc) at this step again.
Note that you need to be using the gold linker for this to work. If you want to force clang to use a specific linker, create a symlink to that linker named "ld" in a special directory called "fakebin" somewhere on your computer, and add the option
-B/home/jeremy/fakebin
to any linking steps above.