Hi, sorry, coming late to this party!
Bra cups. Yes, the ballroom way is to use the foam ones and attach them only at the top inside the leotard (bearing in mind that all those dresses are built over an inner leotard). The downwards and sidewards pull of the leotard holds the cups in place. If you looked inside a Strictly costume, that's what you'd see, and it works fine for small-moderate cup sizes.
However, for more support, they sometimes attach the bottom of the cups to a band of nude elastic like a strapless bra around the back or around the waist as Brenda suggests, or sew in an actual bra, cutting away the straps as necessary where the leotard can substitute. There's a similar strand in the evening wear section here about that. The "decorative" back straps can also help to hold the whole thing in place either directly across or criss-cross the back. Another option - Jacky/MarnieSews uses a shelf bra with cups in her DGD's dresses.
I think the key either way is if you want to attach the bottom of the cups to something, attach them to the body, not to the front of the leotard so they don't ride up.
Carol