When I change anywhere, I always put the diaper into an 8 gallon trash bag, twisting tighly and knotting it closed. It keeps the smell down and is less inconspicuous when disposing in a public restroom.
If you want to avoid suspicion, you have to remember to act naturally. To anyone else you need the diapers and have always needed them, so you cannot appear nervous. Just do what I said above, walk casually out of the stall, throw it away, and wash your hands. Nobody can fault you on that, if they do, you can politely tell them to fuck off.
The same can be said for while changing in the stall. Use the handicap stall, do not hesitate, and change standing up- really not that hard. If you go into the stall and pretend to be taking a shit, people will get suspicious if they are still in there when you start removing the diaper.
Go in, take care of business, and get out.