I would like to transfer my Firefox mobile bookmarks to my desktop and would prefer doing it without using Firefox sync or any cloud-based extension.
Is there a way to export Firefox for Android bookmarks to an HTML file?
As of 2019, Firefox for Android has no built-in support for exporting bookmarks.
However there are some workarounds/alternatives:
I do not have enough reputation to add a comment to Paul Benedict's answer hence I am forced to add this "comment" as an answer...
Paul's "Workaround/alternative 1" (which links to the "Chosen Solution" on the Firefox Support Forum) suggests using "Firefox Sync for Android" (and yes, I do realise that the OP explicitly requested a solution that does not involve using Firefox Sync). This will NOT work as desired, because although you can sync your mobile bookmarks over to desktop firefox, Desktop Firefox's "Export Bookmarks to HTML" does NOT "export mobile bookmarks when exporting as HTML" (note that bug is almost 3 years old now).
For anyone who do not object to using Firefox Sync, either:
There is a way to export bookmarks to a file (not HTML, though) if that is enough for you ("you" being whoever ends up here from a search engine, as this question is already rather old). It might or might not be a practical solution depending on the amount of bookmarks that you have.
If you go to Bookmarks view in Firefox for Android (in my case the first item in the main menu), you can long-press on the first item to select it, and then proceed to selecting all of your bookmarks one by one. (I did not find a way to select all, so this is where "it might not be practical for you" comes in). You can then click the sharing button in the menu bar, and select a best fitting way of storing the bookmarks from the alternatives that are presented to you.
It's hard to be more precise here as the sharing alternatives depend on the apps you have on your phone, but I was able to simply store the text on the clipboard, and then paste it to a simple text file using an installed text editor. You might have other, more practical alternatives as well. With this method the bookmarks are "exported" as a simple list of URLs (plain links) so you will lose any meta data like bookmark names that you might have stored in Firefox.