The key to cutting folded fabric into strips without a "V" in the middle is to make sure that you are cutting exactly a 90-degree angle to the fold. The fold can be anywhere in the fabric (even bias!). As long as you make sure that your cutting ruler is exactly 90-degrees from the fold, you will have a straight strip.
There are different ways to make sure that your ruler is exactly 90 degrees to the fold. What I do is use another ruler -- straight, square, or triangle -- and butt it up to my cutting ruler. If the line of the fold matches the line on the second ruler, and if that second ruler is butted up perfectly to my cutting ruler, I know there will be no "V". It helps if the secondary ruler is long enough to allow you to line up at least 12 inches of the fold and tall enough to butt against your ruler for 12 inches; the longer each of these is, the more likely you are to be accurate.