If you are brushing a water-based finish over a water-soluble dye, you should be aware that the finish can dissolve the dye and the brush will pick it up and cause streaks. To keep this from happening, seal the wood first with another finish that doesn’t contain water—for example, shellac, varnish or lacquer.
Another solution is to spray the first coat of water-based finish. If you don’t have a spray gun, you can usually find aerosol water-based finishes in home centers and paint stores. As long as the object isn’t large, the aerosol should work well.