Can you buy grass bags for older lawnmowers?

You will need the make/model and serial number of your lawn mower. There will be a metal plate somewhere on the mower with that information. Then do a web search using those numbers and what part you need. There are tons of folks who will be glad to sell you the part. Sears included so if it's a Sears mower go to their site and search there. Even Amazon may carry it.