Your bike has a tiny top-tube which is level and would make a great handle. One method is to stand by the left-side of teh bike (so you're away from the potentially oily chain) and bend at the knees. Grab that little bar with one hand nearer the bike, and use your other hand on the saddle or handlebars for support and balance.
Keep your back straight, and lift with your legs.
If you don't want to/can't pick it up, then a bike will roll backward fine - only downside is that the pedals will revolve as you push it backward and can hit your knees/shins.
Getting it up the stairs would be harder than wheeling it downward where gravity is on your side rather than resisting you. At the stairs either let it roll down while you stand beside, using the brakes to slow the descent, OR set the bike sideways on the top step and lift each end down one step at a time.
@hursey's suggestion was about pulling the bike up so it is balanced on its rear wheel only and you're using two hands on the bars, in combination with the rear brake lever to control the unbalanced bike. Something vaguely like this:
Bodged photo to show idea
To get here, you stand beside the bike, and put both hands on the bars like you're riding. Then clamp on the rear brake only. Pull back on the bars and the front wheel will come up. When its balanced you should only need small inputs to hold it.
If it all starts getting away from you, lock up the rear brake again. Gently release the rear brake and push the bike around - you should be able to rotate in the hallway and face the exit door. Note you can't steer by turning the bars, you have to twist the bike around the vertical axis.
Then lock up the rear brake again and lower the bike's front down gently. Since you're only lifting the front of the bike, its only half the weight and only until the bike gets balanced over the rear wheel.
Notice in photo, the model has her knee against the saddle, providing another point of stability.