I want to launch an interactive shell that has special aliases and functions, not the ones in the user's ~/.bashrc.
Just specify a different start-up file:
bash --rcfile /my/custom/bashrc
bash --rcfile <(printf %s 'my; commands; here')
Variant question: I have a script that sets up an environment, and I want to give the user control at the end of it.
Put exec bash at the end of it to launch an interactive shell. This shell will inherit the environment (which does not include aliases, but that's OK, because aliases suck). Of course, you must also make sure that your script runs in a terminal -- otherwise, you must create one, for example, by using exec xterm -e bash.