When using a drill to scribe the center lines you use one a few hundredths smaller that the steel thickness. Scribe one line and flip the blade over. Scribe again. Now you have two parallel lines to grind towards. For every .01" less than the steel thickness the two lines will be .02" apart. So, if you want the edge to be .040" on a piece of 1/8"/.125" steel, use a #36 or #37 bit (about .105"). Realize that steel marked 1/8" will be anything from .120 to .150". Unless precision ground it almost surely won't be .125". Most steel comes about .015" oversize.
For no-warp exact-thickness steels, order precision flat ground stock. This is what many folder makers use. However, if you are grinding bevels and all other features on a blade you will end up grinding nearly every surface, so you really only need flat-ground stock. Most of us don't even get that unless the steel will be hardened as a bar with no profiling.
It really doesn't matter how much the lines are apart, though. They are a guide in grinding the bevels. You can grind to a nearly sharp edge and then just "dull" the edge back a minute amount to get the desired edge thickness per-HT. A few strokes with a fine-cut file will drop the edge back to .040".
TIPs:
1) Make or buy an edge scriber. It will follow the edge regardless of any warp. This will give the best edge lines for grinding.
2) When starting the bevels, grind the edge at about 45° to the scribe lines (I take it to the center). This gives a visual reference of how much you need to tilt the blade to make the bevels go from the top of the grind to the edge. It also greatly preserves the visual center line. You can accidentally grind past a scribed line, and they can be hard to see sometimes.
3) Final tip to a new maker - Get a cheap $10 micrometer from HF or Amazon. Measure a bunch of knives in your kitchen, your pocketknives, and some commercial hunting knives (you can look those thicknesses up online.). You will quickly find out that 1/8" steel is twice as thick as most all knives. Kitchen knives range from .040" to .060". Hunting knives are .060" to .010". Pocketknives range from .050" to .090". This is why many of us don't grind any bevels before HT. If Iam making a .060" thick kitchen knife from .070" stock, and I wanted the edge to be .040" before HT ... I don't need to grind any bevels before HT.
Too thick is probably the number one thing wrong with most first (and sometimes 100th) knife. It affects weight, balance, ergonomics, and cutting ability. You want fat to chop and thin to cut. Distal taper is also very important on most knives, and it will allow for somewhat thicker stock, but no one really wants a .125" thick tang on a chef's knife.
4) Many new makers learn to grind a perfect bevel with the "Bubble Jig" IT is a bevel angle measuring tool used to grind the bevels by showing you a bubble to watch as you grind. The maker, Fred Rowe, sells them in The Exchange ,as a very reasonable price.
Final comment on new knives being too thick and heavy - I had a machinist ask me to look over his knife that he made 100% on the mill. He made a beautiful bolster release auto. It had a razor sharp 4" blade that was .200" thick. The blade and frame were O-1. The scales were milled from 1/4" thick carbon fiber. The knife was about 1" thick side to side. It was very heavy (I have made large hunting knives that weighed less). When asked to critique it I complimented him on his machining skills and precision fit and finish. I said the blade's length and thickness, knife overall thickness, and weight were serious issues, though. He replied that he wanted it strong and didn't want it to ever break. I agreed that he was right about that, because no one would carry a 1/2 pound knife in their pocket.