Didn't you get a manual with your camera? Page 84 of the K-1 Mark II manual explains exactly how to use Astrotracer.
http://www.ricoh-imaging.co.jp/english/support/man-pdf/k-1-2.pdf
Note that timed exposure in Bulb mode is only one option (the default, I believe). You can press the green button and switch to a true Bulb mode with Astrotracer active. In that case, you can hold the shutter open for any exposure length you like up to the maximum that the camera shows you on the LCD, which depends on the lens you use and where in the sky you are pointing. And the minimum exposure time becomes as quick as you can press the shutter button twice in a row. In other words, much shorter than ten seconds. Practically speaking, of course, you would likely use an external intervalometer to set the exposure time in that mode, hence one second would be the practical minimum exposure time.
MossyRocks spoke of the stars in the Pleiades not saturating at 10 seconds. While that depends on the aperture of the lens you use, it is true enough for me using a 300mm lens at f/5.6. But on one occasion while shooting the Pleiades, I did need to use less than 10 seconds. It was when Venus was in the same field. I used exposures down to 3 seconds but Venus was still blown out.