@Andrew Swales In the wild with the radio telemetry study of my colleague that I mentioned it was found that they were entering the shallows of quite deep bodies of water like large made made ponds during the dry season and spending quite some time in these areas.
As you have said I do think it is more "bathing" type behaviour rather than swimming and I haven't actually heard of them crossing rivers or things like that (though it wouldn't suprise me if they do as they have a lot of upper body strength and there is still an awful lot that we do not know about their ecology and behaviour).
The only zoo I have seen with a pool big enough for anteaters to truly swim is San Antonio Zoo. They are housed in a large aviary with about two thirds water and one third land. I was there one summer when two anteaters were on display and one went for a swim - not a bathe or a dip - but a true swim for the length of the pool. Here are the photos of it getting in to start the swim:
