I have been having ecgs for the last 25 years for congenital heart disease, and sometimes wear a bra and sometimes i dont for an ecg. It depends what kind of stickers they use. If they use the round ones that the wire clicks onto i wear my bra and they just tuck the sticker s unerneath if necessary. If they use the square stickers that have tags on them for the wire to attach to then they cant practically do it with your bra on.
With ECHOs I think they have to take the bra off because they will need to run the instrument all over your chest, in order to see your heart from different angles.
I've always had to remove everything on top, especially if they're doing a 12 lead test. Some of the leads go right in the middle and under the left breast and on the side. A bra would get in the way and probably cause a bunch of artifacts on the reading every time you took a breath.
And I can't imagine doing a echo with a bra on. They use all that gel junk and slide the transducer here and there on your chest. Trust me, they don't care about your chest. When I had mine done, the tech was focused on the monitor, watching my heart and making recordings of this and that. When he was done, he tossed me some tissues and said, have a nice day.
I've had a TON of EKGs done and most of the time they have me remove my bra, sometimes they let me leave it on.. I've even had some techs go as far as making me remove ALL metal though (rings, ear rings, even my jeans because of the buttons). I do think it's done mostly for convenience to the tech but there could be something in metal that messes with it.