The beats are audible at lower frequencies because your ears do in fact pick up phase information, but only at these lower frequencies.
When a sound enters our ear, we magnify it via mechanical oscillations of bones and hydraulic effects, ultimately causing vibration in a thin film in our inner ear called the basilar membrane. Different sections of the basilar membrane will vibrate in response to different tones. The basilar membrane is connected to thousands of small hairs, themselves connected to mechanically-sensitive ion gates. Oscillations of these hair then trigger the ion gates. The ion gates send electrical impulses down neurons to our brains.
Empirically, it is observed that these nerve impulses almost always begin at the peak amplitude of a vibration of the basilar membrane. Thus, if our two ears receive sound with different phase, they will fire nerve impulses at different times, and our brains will have access to phase information.
An interesting demonstration of this was given by Lord Raleigh in 1907. He theorized that phase difference detection between the ears was a key component to our ability to localize sound. When Raleigh played two tuning forks that were slightly out of tune, so that the phase oscillated, his found that human perception of the location of the sound oscillated from the left to the right of the listener's head.
At high frequencies, we lose phase information. This is because of uncertainties in the exact time of arrival of a nerve impulse. A typical nerve impulse lasts several milliseconds, so above 1000 Hz the uncertainty in arrival time becomes comparable to the frequency itself, meaning we lose phase information. It turns out that we mostly lose the ability to localize sound in the range 1000 - 3000 Hz. Above 3000 Hz, different physiological mechanisms related to the "shadow" of your head allow us to localize sound again.
Reference:
http://en.wikipedia.org/wiki/Action_potential
The information about Rayleigh's experiment and firing at the peak of oscillations is from chapter 5 of "The Science of Sound" by Rossing, Wheeler, and Moore.
It's not so much that the bass frequencies go long distances as that the high frequencies get absorbed and don't.
Say that the dimensions of your room are 30 feet x 20 feet. Your room will be pretty good at scattering sound that has wavelength shorter (i.e. frequency higher) than $\lambda = 20$ feet. Since sound travels at around $c_s = 1000$ feet per second, this is frequency $f = 50\textrm{Hz}\;$:
$$\lambda = c_s/f$$
$$ \textrm{20 feet = (1000 ft/sec) / (50 /sec)}$$
So you can expect that frequencies less than around 50Hz will escape your room better than the high frequencies.
When you see the sun go down the sky turns red because the red (low) frequencies get absorbed less than the blue (high). And as you'd guess, it's for the same reason. Except for things that are specially designed (or lucky), anything that absorbs a long wave length (low frequency) is big enough to also absorb the short wave lengths (high frequencies).
Of course, just as with colored glass, it's possible for matter to reverse the situation and have some low frequencies absorbed while the high frequencies penetrate. But it's not the way to bet.
Best Answer
You don't.
You actually hear the high frequency notes from headphones. The bass really doesn't travel at all well, but the attack noise from the drum or bass guitar is what leaks from headphones.
This is why on the tube you hear "tsss tsss tsss tsss" and very little else.
From @leftaroundabout's answer on the post that valerio92 linked: