I I think bluetooth is likely to be the culprit when it comes to battery life - although it does sound like you aren't getting as much battery life as I'd expect. Actually Apple states 40 hours audio playback! But if you look on their site, there are certain settings required - and they don't mention bluetooth speakers. click here for your name, I'm not a Windows user, but I'm assuming that at one point you have entered your name into the settings of your computer. The iPad will have taken it from that.
Why do you think the iPod might be used - did you buy directly from Apple or someone else?
Apple has some tips for improving battery life here: click here you know if the iPod is running iOS 9? It should be updated to the latest software.
Read this post, it might help: click here