Depends on where your room is at Pop, your walking speed, and whether or not they have a line at AoA! It also depends on if your room is ready and if you are going to take your stuff to your room - or if you are going to have to leave stuff at Bell Services. Lots of variables. Or if you are going to ask if a room is ready now - instead of waiting for whatever room they pre-assigned you to.
For me - assuming what I typically see at Disney - between exiting my room at Pop - to either 1) done at Bell Services and headed to bus stop or 2) opening my hotel room door at AoA - I'd say 45 minutes.
30 minutes - if all things align and the walking distances are not too bad (maybe even 20 minutes!). An hour - I waited for service more than I had hoped at some point.
Me - I'd budget an hour from leaving my hotel room at Pop to being at the bus stop at AoA to head to a park. If it all happens in less time - I'd be happy that my morning is going smoothly.