If you have Premium bought from the App Store there would be no code base in there to show any ads while in BaconReader. If you are in the Pro there is slightly higher of a chance but that just needs to be clarified through the App Store by going through Already Purchased on the device. Those are tied to specific Apple IDs.

On Android, Google Play had an update that messed up specific areas... and we got the backlash for that. /u/onelouderchic happens to explain it really well here:

You will need to go to the play store under each account to figure out which one you purchased under. After that, remove all other accounts from the device, load BR and google should then recognize your purchase. You may be able to add the other accounts back to the device after that. Here's the reference info again if you need explaining the issue:
Copy/paste from another thread about this: Do you have multiple accounts in the Google Play app on your device? If so, this is a bug in Google's Play in-app billing version 3. They have a bug where if you have more than one account in your Play app, the purchase won’t be properly recognized.

You can find the bug report here: https://code.google.com/p/marketbilling/issues/detail?id=76 This only affects the V3 version of in-app billing that was integrated in the 4.0.4 version of the app and not the previous V2 (see https://support.google.com/googleplay/android-developer/answer/6090268?hl=en), but since Google has ended support for V2, we had no choice but to update. If you remove the second account that the purchase was not placed under, Play should recognize the purchase again.

If you do not have multiple accounts in Play, after an update, it can sometimes take a few minutes for the Play store DRM to run for V3 and for Play to recognize that the app has been purchased remove the ads. In that case, the first thing I'd do is reboot your device. If that doesn't make a difference, I would go in to the application manager/manage applications in your device settings and locate the Play app and then clear the cache for Play. This should force the Play app to re-query their database for purchases.