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.
Do low frequencies carry farther than high frequencies? Yes. The reason has to do with what's stopping the sound. If it weren't for attenuation (absorption) sound would follow an inverse square law.
Remember, sound is a pressure wave vibration of molecules. Whenever you give molecules a "push" you're going to lose some energy to heat. Because of this, sound is lost to heating of the medium it is propagating through. The attenuation of sound waves is frequency dependent in most materials. See Wikipedia for the technical details and formulas of acoustic attenuation.
Here is a graph of the attenuation of sound at difference frequencies (accounting for atmospheric pressure and humidity):
As you can see, low frequencies are not absorbed as well. This means low frequencies will travel farther. That graph comes from this extremely detailed article on outdoor sound propagation.
Another effect that affects sound propagation, especially through walls, headphones, and other relative hard surfaces is reflection. Reflection is also frequency dependent. High frequencies are better reflected whereas low frequencies are able to pass through the barrier:
This is and frequency-based attenuation are why low-frequency sounds are much easier to hear through walls than high frequency ones.
Frequency Loudness in Headphones:
The above description apply to sounds that travel either through long distances or are otherwise highly attenuated. Headphones start off at such low intensities already they don't travel long enough distances for attenuation to be a dominate factor. Instead, the frequency response curve of the human ear plays a big role in perceived loudness.
The curves that show human hearing frequency response are called Fletcher–Munson curves:
The red lines are the modern ISO 226:2003 data. All the sound along a curve is of "equal loudness" but as you can see, low frequencies must be much more intense to sound equally as loud as higher frequency sounds. Even if the low frequencies are reaching your ear, it's harder for you to hear them.
Headphone sound is doubly compounded by the difficulty of making headphones with good low-frequency response. With loudspeakers you can split the job of producing frequencies among a subwoofer, a midrange speaker, and a tweeter. For low frequencies subwoofers are large and have a resonating chamber which simply isn't an option with headphones that must produce a large range of sound frequencies in a small space. Even a good pair of headphones like Sennheiser HD-650 struggle with lower frequencies:
So if it sounds like high frequencies travel farther with headphones, it's because headphones are poor at producing low frequencies and your ear is poor at picking them up.
Best Answer
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.