In short - no. There are not even no sources, 1 l of semen amounts to about 250 ejaculations of 4 ml, so for bathing in a (todays) standard tub with a filling of 140 l, she would have needed 35000 cumshots.

I'm not even going to start explaining how that would be a nightmare in logistics and preparation even if she had 35000 "semen slaves" available (the strenght of about 6 roman legions at that time).

Even the more common theme of her bathing in donkey's milk is based on Nero's second wife, Poppaea Sabina, of which Cassius Dio, judging her wastefulness, wrote: "The extremes of luxury indulged in by this Sabina I will indicate in the briefest terms. She caused gilded shoes to be put on the mules that drew her and caused five hundred asses that had recently foaled to be milked daily that she might bathe in their milk." (Cassius Dio 62, 28, 1)

The image of Cleopatra bathing in milk did only become popular in the 1930's, when Cecile B. DeMille first released The sign of the cross (1932), which features Claudette Colbert as Poppaea bathing naked in milk, and two years later, starring the same lead actress, Cleopatra (1934).

While I did not do any research on in which movie the idea of a semen bath came about... well ... I think you know where to research something like that.

Edit: *image, *research