You can get it to work with export -f, as @kojiro's points out in a comment above.
# Define function.
my_func() {
    // Do cool stuff
}
# Export it, so that all child `bash` processes see it.
export -f my_func
# Invoke gnome-terminal with `bash -c` and the function name, *plus*
# another bash instance to keep the window open.
# NOTE: This is required, because `-c` invariably exits after 
#       running the specified command.
#       CAVEAT: The bash instance that stays open will be a *child* process of the
#       one that executed the function - and will thus not have access to any 
#       non-exported definitions from it.
gnome-terminal -x bash -c 'my_func; bash'
I borrowed the technique from https://stackoverflow.com/a/18756584/45375
With some trickery, you can make do without export -f, assuming that the bash instance that stays open after running the function doesn't itself need to inherit my_func.
declare -f returns the definition (source code) of my_func and so simply redefines it in the new bash instance:
gnome-terminal -x bash -c "$(declare -f my_func); my_func; bash"
Then again, you could even squeeze the export -f command in there, if you wanted:
gnome-terminal -x bash -c "$(declare -f my_func); 
  export -f my_func; my_func; bash"