Run a function defined in the bash script in a new detached screen

I was writing a question, but finally came up with a solution. As it might be useful for others (my future self, at least), here it is.

Context

To run a single command in parallel in several detached screens that automatically close themselves, this works nicely:

timeslots='00_XX 01_XX 02_XX 03_XX 04_XX 05_XX 06_XX'    
for timeslot in $timeslots;
do
    screen -dmS $timeslot bash -c "echo '$timeslot' >> DUMP"; 
done

But what if, for each timeslot, we want to execute in screen not one but several (RAM-heavy) commands, one after the other?

We can write a function (in which everything is run sequentially), with an argument in our bash script.

test_function () {

    # Commands to be executed sequentially, one at a time:
    echo $1 >> DUMP;        # technically we'd put heavy things that shouldn't be executed in parallel
    echo $1 $1 >> DUMP;     # these are just dummy MWE commands
    # ETC                   

}

But, how to create detached screens that run this function with the $timelot argument?

There are lots of discussions on stackoverflow about running a distinct executable script file or on using stuff, but that's not what I want to do. Here the idea is to avoid unnecessary files, keep it all in the same small bash script, simple and clean.

Function definition (in script.sh)

test_function () {

    # Commands to be executed sequentially, one at a time:
    echo $1 >> DUMP;        # technically we'd put heavy things that shouldn't be executed in parallel
    echo $1 $1 >> DUMP;     # these are just dummy MWE commands
    # ETC                   

}
export -f test_function # < absolutely crucial bit to enable using this with screen

Usage (further down in script.sh)

Now we can do

timeslots='00_XX 01_XX 02_XX 03_XX 04_XX 05_XX 06_XX'
for timeslot in $timeslots;
do 
    screen -dmS $timeslot bash -c "test_function $timeslot";
done

And it works.