Neither the fist bump nor the elbow bump will do.

The problem is that the old ways are still embedded in the culture.   According to the old ways, a kiss or a hug between male and female, not lovers but friends, was welcome.    Now of course they are not welcome, but we interpret their absence according to the old ways, as a token of rejection.

Maybe what we need is a better new ritual than the bump.   I propose a bishop's blessing fused with direct and sustained eye contact.   Top to bottom and then side to side, from right to left.  (My Jewish friends can find a separate solution.)

The eye contact will be essential to make it work.

But also those saying farewell should be mirror image in the blessing they convey, not "at cross purposes," pardon the play on words.

So who goes right to left?   It can't be based on hierarchy, or age, or gender. We need a convention that is neutral, like the "rules of the road" for sailing craft, which provide that port tack yields to starboard, but if two boats are on the same tack, then windward boat yields to leeward.  Perfectly neutral.  I yield to suggestions.