I see this is on TCM March 10 at noon ( a very rare showing indeed ) and it made me wonder if it played the US uncut. I have a copy of the British print and it features full frontal Judy Geeson skinny dipping and have wondered if this was the way it was shown in the US.
Is there another take of this scene used for US prints?

Not sure what was shown in the US, but certain scenes were shot in both clothed and nude variants. The clothed version has been shown on British television by the BBC, whereas the nude version has played on Australian television.

Oh those cheeky Aussies! God Luv 'em.

Figured there had to be, Judy Geeson is very naked and I could not see this airing on TCM in broad daylight. I am curious about the alternate takes and appreciate the info.
My dvd-r copy is from points unknown, but is likely an uncut TV broadcast ( or did this get a VHS release somewhere ? )

Haven't we established that TCM does censor some of their films? If so, I would doubt that they would air the uncut version of MULBERRY BUSH. I recall that there was some explicit material missing from their telecast of Cornel Wilde's NO BLADE OF GRASS, to cite one example.

The BBC version is cut in the following places:

1- 4m 37s in. Some dialogue ("No hard feelings", "That's what you think") has been cut from the scene in which Jamie (Barry Evans) meets Mary (Judy Geeson).

2- 4m 36s in. Footage of a man removing a condom from a drawer while saying "Not to be used after November 5th 1969. Fireworks night, eh. Better put it in my pocket before it burn a hole in the drawer" has been cut.

3- 71m 6s in. 16s has been cut from the scene in which Mary and Jamie make love - shots of Jamie moving his hand down Mary's body and caressing her leg.

4- 79m 36s to 80m 20s. The scene in which Mary strips and goes skinny-dipping (followed by Jamie) appears here in a censored form that eliminates all nudity, partly through cutting, partly through the use of alternate takes. The scene runs 1m 6s longer in the Australian print.

5- 80m 20s to 82m 12s. Immediately following the above is a scene in which Mary and Jamie talk while sitting by the river. In the Australian print (where the scene runs 24 seconds longer) they are naked; in the BBC print, they are fully clothed.

No longer listed on the line up, perhaps they found they had the longer cut & pulled it? ( or more likely something less dramtic )
Maybe it will turn up late night on the underground show or just late night instead of mid day.

I just found a New York Times review for the film from March 15 1968 and a reference is made to daring nude scenes, so I guess the US did get the extended version.

Good news!
TCM has added this to their September line up as part of the Underground series.
early fri / sat sept 12 2 am est