As long as you are working with a porous material such as wood, you can expect some bleeding. It is kind of inevitable.
My solution is have as much natural contrast between the woods as possible, then let the bleeding happen in the dark stuff.
You have your light strip and the darker wood beside it. You are staining the dark wood. Place your masking tape so it overlaps onto the darker wood about 1/16". Most of the bleeding will happen in this 1/16" zone, giving more stain to the already dark wood. It will not bleed consistently, so there will be some bits of that 1/16" which are not stained.
If you have good contrast between strips to begin with, your eye will see the sharp edge between the light wood and the natural dark but won't notice that color change of the dark is a bit fuzzy due to the bleeding.
This holds up to pretty close inspection, you can see whats going on if you look closely, but from any distance your eye sees a nice crisp contrast and doesn't pick up on the bleeding edge.
Below is a close up i just took. 3/4" wide strips for reference. You can just make out the natural color of the dark strips just above the light strip. Not a great photo, but the best I could do in a dark shop.
I use 3M 2060 masking tape. It sticks to wood better than anything I have found. If you need narrower stripes than you can buy, take a new utility knife blade, stack it on top of a spacer of the desired thickness, hold it down of a flat surface, and spin your roll of tape around the blade to cut the width you need. Spin it enough to cut as deep as you need for the length you need.