There are restrictions, the primary being that the pipe must have pitch to drain in any horizontal run, and cannot have any "jogs" in the line that would prevent complete gravity draining. Some areas also have limit to the length of any horizontal section to a percentage of the overall length of the vent. While there might not be a restriction to the number of bends, there should be one accessible cleanout in the line for every 135 degrees of change in direction.
You should also consider that the 1-1/2" vent allows no room for expansion. If you wanted to add the laundry or another sink in the basement, you would need to run another vent through the roof.
It is always best to locate a place in the house where you can go straight up from the basement through the roof. As an alternative, you can run straight up into the attic and connect to an existing vent there. Where there are no stacked walls to run a vent through, there often are stacked closet spaces where a vent can be run in a corner of a closet and boxed in after the plumbing inspection is completed.