You have changed permissions through your ftp program, right?
Depending on your server setup that isn't enough. Most, if not all, hosts give you the ability to access your site directly either with cpanel or directadmin. That is the part where you can also create databases, or in general where you can manage your account.
Now, there must be something there where you can manage your files, usually called file manager. There you will have a similar structure as on ftp but a few more possibilities.
The important ones for this case would be file permissions and ownership. Where you see the structure of your joomla installation there you would see columns with permissions, uid and gid. The last two must be you (that means you as in your account name) and not apache.
So check those for the booking module and change them to you.
If still in doubt you should really have a look at your hosts documentation.