It seems to me that the bit stream speed is independent of the bit content. If this is correct than should not the jitter be either constant of possible a function of the disc itself (like radial position or burn/pressing quality)?
That was assumed when CD players were first invented. However, many things can affect the accuracy of the clock signal in the DAC. And even the bitsream is variable - error bursts and misreads may be cyclical and perhaps only the digital "preamble" is fairly consistent - so the data may vary in a certain repeating patterns.
Provided jitter is random, it is in general a negligible problem. However when patterns - such as power supply oscillations due to cyclical laser servo movements to track the pits on the rotating disc occur - then we can get non-random jitter. Another major cause of non-random jitter may be the Phase Locked Loop between teh master and slave clock - in this case, the very act of trying to keep the slave clock in time with the master cause oscillatory patterns as the slave hunts back and forth trying to keep in time. These repetitive patterns in clock timing erros cause new oscillatory audio signals to appear in the analog music coming out of the DAC - sometimes called sidebands - non-harmonically related signals. It is these very small (-40 db) but 'correlated' sounds that become audible - usually as hash or lack of clarity in upper midrange and HF (although this may significantly affect the perceptive sound of percussive instruments with low frequencies - like piano or drums - due to the way we "hear")
Anyway - jitter is an analog problem - it only appears upon conversion to analog or, up front, when converting analog to digital.
If you have a perfect clock then you will not have jitter.
DAC's have evolved to have better clocks. Early designs like Meitner used patterns in the digital data called "preamble" to try and achieve a more accurate clock. Others like Lavry used algorithms to maintain a very slow correction pattern on the slave clock that could be filtered out. Since about 2002 the problem has been substantially addressed by "asynchronous DACs" - basically these type DACs ignore the master clock altogther - and in these designs the jitter is totally determined by the clock quality in the DAC along and nothing upstream of the DAC.