THAT RECENT exchange of letters between Sen. Edward Kennedy and Attorney General Griffin Bell has Don Quixote written all over it. The first, from the senator, seemed to beg for an all-out war between the two men because of the way the attorney general had handled a major antitrust case. The second, by the attorney general, seemed to say if that's what you want, buddy, you've got it. But now that the two men are standing all alone on the field of battle, they appear to be looking around and asking, "Who, me?"

It began when Sen. Kennedy charged off in the wrong direction by asking the Federal Trade Commission to investigate the proposed merger of two steel companies. That was dumb, unless he wanted a war, because Mr. Bell had personally approved the merger last summer. The FTC has no business getting into it now unless there was some impropriety in his action. Indeed, as if to make the war certain, the senator's letter implied that just such an impropriety did exist.

When the attorney general read a copy of this letter, which the senator had graciously sent him, that implication pierced his heart. Rising to the challenge, he roared back that an FTC investigation would be "intolerable" and that his relationship with the senator had surely been endangered if the letter reflected Mr. Kennedy's view of his abilities.

It's hard to imagine a better start to a long-running battle between a Cabinet officer and the new chairman of the Senate committee that handles practically all of that Cabinet department's legislation. But once those lances crossed, something happened. Would you believe the two men had dinner together almost immediately and never mentioned the letters? Or that they have discussed legislation twice this week without talking about this matter? That's what their staffs say has happened, anyway.

This implausible story has a degree of plausibility for several reasons. The length of the original Kennedy letter - five pages - suggests he didn't write it personally. The reluctance of his office to release the letters suggests he wasn't looking for trouble and hadn't appreciated the implications of what he signed. Bad staff work, in other words. The protestations of the attorney general, on the other hand, suggest that, because his skin is still a little thin for Washington-style battering, he decided, hastily, that one blow had to be met with another. Add to this combination of overreactions the old Kennedy-Bell friendship - it goes back to the 1960 presidential campaign and runs quite deep - and you can understand why each is now looking for a way to back off.

Our hunch is that the proposed FTC investigation will fade quietly into the November mists (aided, perhaps, by a Kennedy request to cool it) and that the senator and the attorney general will be working arm-in-arm on Capitol Hill in January as if the letters never existed - which they shouldn't have in the first place.