You may find useful this wikipedia page
You can calculate the exposure value with the given formula:
EV = log2(N^2 / t)
N = the f-number (aperture) you will use
t = the exposure time you will use
they both depends on your camera: search a middle aperture for your lens and a time you will likely use (a rule of thumb is that the slower time you should use freehand is the inverse of your focal length (i.e. if you have a 50mm lens, you should use 1/50 of sec))
When you got an EV number, check against the table in page I linked and see if you can convert it in a bulb :-)
Apart it's interesting to measure EV value in itself, frankly I think using a support is anyway a better policy because it also allow you to study composition more at ease. Consider using a monopod if a tripod is too big.
Forgot to mention that the above formula is for 100ISO sensibility, should you use a different setting, you have to correct the EV value accordingly. In the linked page there are the necessary details.