How to make mount --bind permanent?

What do you mean "clogging up /etc/fstab"? The best place to put this in is /etc/fstab; that's what it was made for!

All you have to do is add one line after the first mount:

# <device>                                 <dir>                 <type>  <options>                 <dump>  <pass>
UUID=288a84bf-876c-4c4b-a4ba-d6b4cc6fc0d2  /mnt/device            ext4    defaults,noatime,nofail   0       2
/mnt/device                                /srv/binded_device     none    bind                      0       0

The easiest way is to mount --bind what you need like

mount --bind /home/sda1/Windows/Users/Me/Dropbox ~/Dropbox

Then open mtab

sudo nano /etc/mtab

Copy your line like

/home/sda1/Windows/Users/Me/Dropbox /home/me/Dropbox none rw,bind 0 0

and paste it in fstab so it would mount on reboot

sudo nano /etc/fstab

If you folder is on mounted disk make sure your binding line comes after disk mount

Another solution (which is helpful when you're using LVM and the accepted answer will not work and some may consider more useful since it uses a bit more logic) would be doing something similar to this:

Append the following to your crontab
# crontab -l | tail -1 ; cat /usr/sbin/custom-compiler-mount

@reboot /usr/sbin/custom-compiler-mount

Essentially you would use crond to execute a script on reboot

#!/bin/bash
( until [[ $( (mount |& grep vg0-homevol 2>&1 9<&1 > /dev/null 1<&9) ) ]] ; 
do 
sleep 1 
done & wait;mount -o rbind /home/linuxgeek/experimental/s3/gcc/ /gcc & ) & >/dev/null