While I don't use walnut oil much anymore, it has the great advantage of being readily available, such that the ultimate owner of the bowl can refresh the finish as needed.
But I now mostly use Sutherland Welles Polymerized Tung Oil (recommended above by Vincent) and Sutherland Welles Wiping Varnish (which adds a touch of resin to the tung oil). These finishes are so easy to apply (wipe-on / wipe-off) and are very versatile: satin to gloss, depending on your blends and application methods.
I note that these finishes accord with Seri Robinson's recommendations in her AAW article (a drying oil or Danish oil [drying oil + varnish]) for salad bowls that will have the dressing mixed in the bowl. (I think it is best to cover the possibility that the ultimate owner might mix the salad dressing in the bowl.) Sensibly, I think, Dr. Robinson is in the "once it is cured it is food safe" school, given that she specifically recommends that these finishes include driers so that they cure properly, and specifically warns against "raw" oil finishes because they take ages to fully cure. The above-mentioned Sutherland Welles tung oil finishes have some safe-when-cured solvent, but SW also has their "botanical" line with a citrus-based solvent for those who want safe-even-before-cured.
Chuck, re: the wax and oil you have put on by using the abrasive paste, give the bowl several good rub-downs with DNA or isopropyl alcohol; this is not a complete fix, but it will remove some of the oil and wax and should improve the penetration of the oil finishes.