Here it is again, hope it's not too longwinded :
I use shellac in woodworking but have not used it on handlebar tape. The process is like what Otis describes. The initial coat is thinned down with alcohol and subsequent coats with less thinning, builds up the finish. The key to multiple coats is to apply the finish thinly so as not to create an effect of "encapsulation". The durability of a finish coating (shellac in this case) is not entirely due to thickness of the coating. There is a point where the finish is too thick and will actually wear faster because the supporting substrate is too far away and the thick finish becomes too flexible.
In your case, you shouldn't apply more coats. Instead, just use an alcohol dampened rag and keep wiping it down until you start to feel the texture of the tape. Take a rag, stop the opening of the can of alcohol, invert the can. Wipe the bars with speed and light pressure. The finish might dull and as the alcohol evaporates, turn glossy. This all happens very quickly. Don't use too much alcohol as it will only dissolve and spread the shellac around. Use less ( and lots of rags), speed and short strokes and you can "pull" the excess shellac off. You might be surprised how quickly you can acquire the feel of the technique and attain a level of shellac zen

and how you can control the look of the finish (lower or higher gloss). Shellac dries very quickly because the carrier and solvent is alcohol.
If you start again with fresh tape, thin the first coat 50/50 or less alcohol, brush on quickly. Repeat if there are missed areas. Let dry half an hour or so or until it just stops feeling tacky. Brush on a second coat unthinned, let dry an hour to two, third coat unthinned, let dry an hour to two. I think that should be enough. This is not fine furniture or musical instrument finishing and you want the shellac to soak into the fabric and then enough on top for some durability.
If you want an uber gloss, try this - after the final coat dries, use 600 grit wet and dry paper with a few drops of mineral oil or olive oil and gently polish the bars. It will reward you with a happy and lustrous gleam. In woodworking, the addition of oils and other substances not only increase the gleam and glow, but also gives the coating a certain flexibility.