I have that same problem, but worse. My home is on a very space constrained network drive and I install none of the games there but in another folder instead. I can't use root to bind mount haht folder. The check prevents me from installing certain games, because the rest space on that drive I don't use, is less then the required space, even though it'd fit onto the other drive. This is rather sad.
You don’t need to use bind mount at all, follow this comment https://github.com/ValveSoftware/steam-for-linux/issues/1600#issuecomment-13429489
When installing to the default library, Steam appears to check ~/.local/share/steam/ for free space. However, games are installed to ~/.local/share/steam/SteamApps/. If that folder is on a separate partition/device, the free space reported will be wrong.
The simple fix is to try to check SteamApps folder instead of steam.
A more complete fix may be to try and check the actual game install folder (or SteamApps for GCF games). If that folder doesn't exist yet (likely), it will go up the folder hierarchy until it finds a folder that does exist, and query that one for free space. This will allow for things such as the "common" folder being on a separate partition from the SteamApps folder, and correct free disk space will be noted in all cases.
Of course multiple games installed at once could end up with different free space sizes which would not work very well in the existing Install dialog... so maybe the simple fix is best. Just my 2 cents.
My workaround to this problem (if the free disk space report prevents you from installing games that would fit with the correct free space reported) is to mount your steam partition/drive as .../steam instead of .../steam/SteamApps.