Actually making the parallax measurements must have been incredibly difficult. The star images do not stand perfectly still - in a small telescope such as Bessel's they will dance around in response to changes in the air path as winds blow pockets of warm and cold air through the line of sight. The same effect broadens the images to make them larger than the parallax he was trying to measure. All the measurements had to be made squinting through the telescope and carefully adjusting the screw drive that changes the lens split separation, and fighting whatever the weather was that night. And some nights would have been bitter cold in Konigsberg where he worked - on the coast of the Baltic Sea, as far north as middle Canada. 

Simulation of Bessel's observations
This animation (by G. Rieke) will give you an appreciation of Bessel's accomplishment. Typically, the images of stars are 1 arcsec in diameter, about 3 times the effect he measured. The large proper motion of the star spread the images across the sky. Here we plot a series of pretend star images over 6 months, then a gap, and then a second series. The parallax is the slight tilt of the lineup of images compared with the thin line behind them representing the direction of proper motion (which Bessel also had to measure).

Of course, it all became easier with the first photographic plates. The astronomer could take a picture and measure the positions later in a nice warm office. So Bessel's work was quickly considered to be obsolete:

From "The History of Astronomy During the 19th Century," A. M. Clerke, 1902: "Bessel made known the result of one year's observations, showing for 61 Cygni a parallax of about a third of a second (0.3136")...[He later revised this measure to 0.3483"] Later researches showed that it required an increase to nearly half a second3.

3 Sir R. Ball's measurements at Dunsink gave to 61 Cygni a parallax of 0.47"; Professor Pritchard obtained, by photographic determinations, one of 0.43"

---BUT the modern value is 0.296" +/- 0.004", in much better agreement with Bessel than obtained with photographs! Bessel did a spectacular job!

With further work, we have measured distances to all the nearby stars using parallax. Here is a stereo view of the stars in space near the sunlink to an extra topic