Bubble has native file storage capabilities. Any file uploaded to Bubble can be seen in the Data tab > File Manager. This view respects which files were uploaded to Dev vs Live.
Note, however, that when a file is uploaded to a Bubble app, it is immediately uploaded to the Amazon S3 bucket behind the app. This means that as soon as a file is uploaded, you get a URL to that file that is technically "live", as in anybody with the URL can visit it to see the file. You can, however, make a file private by checking the appropriate setting when uploading the file.