I have been using a Chordette Gem (from Chord Electronics) for a number of years now with very satisfactory results. I can stream music from my iPad, iPhone or iPod Touch with great ease. I have never experienced anything remotely similar to what you describe.
The Chordette employs an A2DP (Advanced Audio Distribution Profile) Bluetooth decoder, and is perfectly suited to all but the most critical listening. It is clearly not quite as good as my Wavelength Brick fed by computer via USB, but the difference (while readily discernible) is certainly not dramatic. I suspect it is largely a result of the difference in quality between the two DACs, although the transmission method (Bluetooth vs. USB) may play a small part.
When I first brought up the topic of streaming music via Bluetooth on the 'Gon some years ago, it landed with a great big thud. Nevertheless, I still think the ability to use an iPad or similar device for both storage and playback of audio (especially now with iPads available in 128 GB capacities) borders on the magical. Perhaps, one day, other 'philes will come around and deign to give it a try.
To my mind, the (very) slight loss in quality is easily outweighed (most of the time) by the tremendous increase in convenience. Certainly anyone looking to assemble a high-quality, compact (or portable) system (e.g., iPhone, Bluetooth receiver, powered speakers) ought to give this approach some serious thought.
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