Apple - Switch Between Apps With Alt-Tab / Command-Tab on iPad or iPhone using Bluetooth Keyboard

No, there isn't a way to do this. As an alternative, I would suggest enabling multitasking gestures (Settings > General > Multitasking Gestures). With them on, you can switch to the next/previous app with a four-finger swipe, instead of bringing up the multitasking bar. You can actually swipe through all of the apps in the multitasking bar, in the same order (order of last use). Note that getting to an app through this gesture does not change their order, so if you swipe left to get to an app, you will swipe right to go back.

See here: http://richmintz.com/2011/04/ipad-app-switching-using-your-bluetooth-keyboard/

I haven't tried it, but if your keyboard has a home button, you should be able to double click it to get the task switcher up. So it seems it should be easy.

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Method copied from source

First, you activate VoiceOver on the iPad, and specify that a Home button triple-press will turn VoiceOver on or off. Then, you just learn a few simple commands and practice, and a lot of common quickie things (like app switching, scrolling through web pages, etc.) become possible without taking your hands off the keyboard. This is most useful when, e.g., you’re writing a blog post on the iPad, in the WordPress app, using the keyboard, and you want to hop over to a web page for a second to check something. Now you can do that without your hands leaving the keyboard, as follows:

• press ctrl-opt-H twice to bring up the app switcher
• press right-arrow to move to Safari, then ctrl-opt-spacebar to tap
• press opt-down-arrow to scroll in Safari (or, if needed, right-arrow to move to the page selection button, etc.)
• when done, switch back, via ctrl-opt-H twice, then right-arrow as needed, then ctrl-opt-spacebar to tap

As of iOS 9 the ability to switch between apps is included in the operating system. Just hook up a keyboard and press command+tab to switch between apps.