You need to use the public folder in dropbox that lets you use "raw" urls. The sharing links will not function for what you want.
Public are available for any file within the "Public" folder in your main dropbox folder. The URL leads directly to the file since it is for public access.
[noparse]https://www.dropbox.com/[/noparse]
u/
<user ID number>/
pathto/file.txt
e.g.
https://www.dropbox.com/u/98931/maps/TLO/01_The_Lonliest_Outpost.jpg
Share links are for any file that is not in public, and each file has a unique key in the URL that leads to a page for viewing, because they are not supposed to be easily accessed by the public.
[noparse]https://www.dropbox.com/[/noparse]
s/
<unique key>/
filenamewithoutpathinfo.jpg
e.g.
https://www.dropbox.com/s/ogmxes2y1xh78z8/015-stairs.jpg
and
https://www.dropbox.com/s/iwb31wznedkw2ed/025-mainframe.jpg
If you don't have or deleted your public folder, just remake it and dropbox will recognize the name.
Inside the public folder you would want to follow the structure Volcomator described. sv_downloadurl expects to be pointed towards a TF root folder.
So If you have your map at C:\Bob\My Dropbox\Public\fastdownload\maps\2fort.bsp.bz2
then sv_downloadurl should be [noparse]https://www.dropbox.com/[/noparse]u/
<userid>/fastdownload
Also note, you might want/need to use http and not https since I'm not sure if Source will work with a secure connection.
And last, just make sure you're doing this for friends or a low-traffic server, because it would be possible to use too much bandwidth and have your dropbox public access suspended for the month.