The best thing to do is to put saddle strings on all your western saddles. Do they have conchos or screws where the strings should be? If so, you can unscrew them and put little metal "D"s under the conchos and screw them back on. Then you can add strings.
A well-stocked tack shop or saddle repair place should be able to help you with the parts. I trail ride myself, so every saddle I get must have at least two sets of good, long saddle strings at the back of the saddle, and preferably in the front too. But that is usually easy to remedy with some saddle strings and some metal "D"s. Then you can tie on your saddle bags.
I don't ride English, but English saddles have two "D's" on the same side because there are little English saddle bags that are made to fit just on that one side of the saddle. I think they are called a sandwich case if I am not mistaken.