As of version 1.6.5 of The Bard's Tale on the Google Play Store, the game now supports cloud syncing of your most recent saved game (via Google Play Games).
If you are logged into your Google account, then starting the game should show a small Google Play Games notification and you should also see a Google Drive sync icon next to your latest synced saved game file. We do recommend keeping multiple saves as backups, however, just as a precaution.
If you do not have the Google Play version of the game or are running an older version, you may be able to sync save files on some devices by using an app like OneDrive, Dropbox, Google Drive etc.
On Android, your save files should be stored at a directory that is something like (varies device-by-device):