using a Bash variable in place of a file as input for an executable

You can use the following construct:

<(command)

So, to have bash create a FIFO with the command as the output for you, instead of your attempted -i ["${inputData}"], you would do:

-i <(echo "$inputData")

Therefore, here is your final total command:

executable -v -i <(echo "$inputData") -o outputFile.eps