This step is optional, depending on whether your bowl is intended to be decorative or functional, but in either case I think the lacquering step makes it look much nicer and has a similar effect to "staining" the wood. Here you will mix one part linseed oil with two parts mineral spirits. One cup of the solution should be several times the amount you'll need; I was doing this by ear and ended up making much more than was ultimately necessary. You should be able to get by even with just a third of a cup.
Using a 1 ½-inch paintbrush, coat the entirety of the inside and outside of the bowl with the linseed oil solution. For full waterproofing, I would suggest five or six coats, possibly more. Drying time for each coat could take anywhere from half an hour to two hours, depending on humidity; I used a hair dryer to speed the process up, to no ill effects. Each coat should be applied once the previous one has dried.