It looks impossible to disable monitor mode for an interactive bash session with command-line options/arguments at invocation time, unless you cheat. I determined this by digging into the source code, primarily the files shell.c and jobs.c. I cloned the repo locally with git clone git://git.savannah.gnu.org/bash.git so that it was easier to search.
It's impossible to disable monitor mode at invocation time because the bash startup sequence enables monitor mode after processing the various options/arguments. Even if you invoke bash +o monitor, where bash will temporarily set the option in the parse_shell_options function, it later calls a function named set_job_control (again, when in interactive mode) which sets the global variable "job_control" to true (the value of the "interactive" argument).
Note that the potential +O shopt route via the run_shopt_alist function is a dead-end, despite the interactive shopt command being able to disable monitor mode with shopt -o -u monitor, because monitor mode is not a native shopt option.
The cheat method relies on an external file; you'd create an alternative bashrc file containing set +m (and optionally sourcing your real ~/.bashrc), then invoke bash as:
bash --rcfile /path/to/that/alternate_bashrc_file
This works because the rcfile parsing is done (with the run_startup_files function) after set_job_control is called, so it's able to finally set the shell option.