If you treat the PDA as simply a display, then you can change your way of thinking about what data actually needs to be sent. It only needs a single trace of data, the width of the display, up to 30 times per second. If we assume 8 bit samples, and a retina display width of 960 columns, then you only need to send 960 bytes 30 times a second, or 28.8kbytes per second. If you are fine with 10Hz update rates, then the link only needs to handle 9,600 bytes per second. When the user zooms in, or changes any of the parameters of the measurement, send the new parameters to the microcontroller, and have the microcontroller prepare the data so you only need a low data rate stream to display the data.
If you want to do analysis on the PDA, then you'll have to send a whole chunk of data, and that's simply going to be slow.
But the more analysis you do on the microcontroller side, the less data you have to send, and the more frequently you can update the display.
Keep in mind that fast bluetooth data links will not connect to iOS devices (iPod touch, iPhone, iPad) without fulfilling the requirements of the Apple Made For iPod program, or jailbreaking the iOS device. This is why many similar devices are using wifi.
If you cannot reduce your data rate, and need the PDA to have full access to all the data with no breaks, you should skip bluetooth entirely and use wifi. Inexpensive wifi adaptors might only handle low data rates, but there are wifi modules that will provide more bandwidth.
This easiest way to do this is to buy a bluetooth module which has serial port profile built-in to its firmware (Roving networks/ panasonic etc have such modules). Assuming your "device" has a microcontroller, the microcontroller could communicate to the BT module via some communication interface (say UART) to transmit and receive data. At the mobile phone end, you need to write an App which will connect and pair with the BT module in your device and once it establishes a stream, your App can transmit and receive data with your device.
This is quite straightforward, I was able to do this and transfer files from my device to an android phone in a week of tinkering.
Best Answer
If it's a good scope, you'll see nothing at all, just a flat line representing DC..
Ironically if it's an inferior scope with incompetently designed input amplifiers and the signal strength is high enough, you may see a step in the flat line when the poorly filtered RF carrier is demodulated by nonlinearities in the amplifier, but that will only tell you the presence of carrier and nothing else. And if the carrier is continuous, you won't see the steps, so you'll never know it's there.
This is the same phenomenon as AM radios and landline telephones picking up a distinctive "dud - dududud - dududud" noise from a GSM phone on the same table.