Bash, execute command but continue with interactive session
If what you need is only a line or two, you can use the cool bash feature of "Process Substitution"[1] to provide it right on the invocation line. e.g. (to run a bash in a specific python virtualenv):
bash --rcfile <(echo '. ./pyvenv/bin/activate')
multiple lines are not a problem, nor is using vars or helpers:
bash --rcfile <(echo echo "Starting at `date`"; echo cd $HOME)
[1] man bash
and look for "Process Substitution". Note that this is not supported on all systems, but it should work on all Linux.