As others have stated, it really depends on why you want to learn quantum mechanics, and how deeply you want to learn it.
(1) If you want to learn it as badly as you want to watch a movie at the movie theaters (i.e. not that badly - you're just mildly interested), then I'd recommend, aside from the books already mentioned, Mr. Tompkins in Paperback by George Gamow. It's a classically wonderful story book that plunges you into the wonderland of modern physics (up until the mid 1900's though). Also, I'd recommend watching a bunch of youtube videos of Richard Feynman. Richard Feynman (1918-1988) was a theoretical physicist with an extremely interesting personality and view of the world. Watching videos of him will get you into science and critical thinking. Finally, reading The Quantum Universe by Hey and Walters will give you what you want. (Beware! There's a book by the same title written by Brian Cox which, in my opinion, isn't that great)
(2) If you want to learn it to scratch it off your bucket list (i.e. you're more than mildly interested in it - it's always attracted you, but you have many more primary interests), I'd recommend to go through what I mentioned in the previous paragraph, and then go through The Theoretical Minimum by Susskind and Hrabovsky. Then, maybe if you're up for it, pick up Introduction to Quantum Mechanics by Griffiths.
(3) If you really want to learn it so badly that you're willing to embark on a life changing journey to truly understand the beauty of quantum mechanics and possibly many other advanced topics of physics, this page is designed for you. Also, once you go through quantum mechanics for the first time (if you do), watch this lecture by Sidney Coleman titled "Quantum Mechanics in Your Face". It'll give the right way of thinking about both quantum mechanics and classical physics.
If you're in between (2) and (3), I'd recommend taking a look at The Road to Reality by Penrose. It's huge, but it might be (a) well suited for you given your background, and (b) the type of journey you're looking for.
Also, as others have stated, the only way to correctly communicate the ideas of quantum mechanics is through the mathematics on which the theory is built. Why this dissuades people so much is because you actually have to think, and most people enjoy having ideas given to them in a way their mind is already accustomed to. That's exactly why I recommended Richard Feynman videos (his books are great too) in (1). If you can learn to appreciate critical thinking and intelligence, the mathematics will become mental masturbation. Blatantly put, the only real way to learn quantum mechanics is to embark on the journey described in (3), and this is more than possible if you can find the motivation through sources like those outlined in (1).