Headphone recommendations?

Your Right Bluetooth has issues with ultra low Bass.

So does CD, oddly though not Mp3

Ie Workload.

And your right the Best option is speakers or Headphones/

  Ps Radio_ sometimes broadcasts in sperate channels

  So that for Example AM 'style' Best for Voice: but not audio.

  Thus mixed, transmission standards, 

This is also a feature of I player.

And maybe head set detection. Etc..

Sony MDR-7506 

You won't get anything better than those for function, comfort or quality.

And less that 100- 

AKG makes a closed ear headphone (actually semi-open) that encircles the ears. AKG is known for accuracy so it is not artificially bass heavy. It is so accurate that studio engineers wore them as early as back in the 1980s because accuracy is very important to them. They used to cost a lot more in the 1980s when they were a company from Austria, but they were later sold to Harman Kardon of the USA and now Samsung owns Harman Kardon. Now the AKG K240 costs less than a hundred bucks, less than it did when I bought one in the 1980s mail order from Illinois Audio (back then the cheapest place to buy them but they have been out of business for a long time)  In fact, Amazon has them for $50 right now. Great deal. It has thousands of near perfect positive ratings. I recommend them over the more expensive and less accurate Japanese brand headphones. 

Sennheiser is also a good brand and it is known for its on the ear designs, which rests on top of the ear. Some people find it more comfortable than the closed ear design. I recently bought a pair of Sennheiser wireless (not bluetooth) headphones and it is also a closed ear design. The closed ear design makes it less likely to fall off the ear and drop to the ground when you lower your head. I had a Sennheiser on the ear wireless headphones and it fell into the water and got damaged when I bent down over a pool of water. The closed ear design however is less comfortable in hot weather and it can make you sweat if you wear it a long time because the heat coming off your head is trapped between the headphone and the ears. You can take off the headphone and let the heat escape and then put them back on again periodically to prevent sweating. 

amazon might have them, they have everything

I have a pair of Audio Technica ATH-M50's that I've had for a number of years and that I would buy again.  They're a little out of your price range but there's a less expensive model, the M30's.  The only thing I don't like about them is they can get somewhat uncomfortable after prolonged wearing.