Yes it will travel!!!!! esp if you have ants. Some Broms are more susceptible and you may find treatment impossible just try to keep pups clean(er) and toss the adults if they are heavily infected once the offsets are capable of surviving. If you only have a small collection then early treatment, follow-up could resolve the problem. Once the adult scale are dead they can be removed with a soft tooth-brush or hosing.
This was the subject of an earlier post, I found this article on a canola-based white oil that breaks down. Don;t use regular white oil.
I've also started using a systemic granule when repotting but care is needed if you have frogs etc. (or well, kids, dogs, cats)

Here is a link that might be useful: Dr Bob's salad dressing

Thanks Alison,
A couple of these are quite infested, so I think I will take your advice and toss a couple and have a look at the canola oil option for the couple that are not too bad. It is a pity because the 2 that are really infested were quite nice Broms. What systemic granules do you use? I will certainly take more care when inheriting Broms from now on. Also which ones are more susceptible, from these ones I assume they are the Neo's.
Michael

Michael with a lot of patience you can clean off a lot of scale if they are nice specimens -I use a bamboo skewer and just scrape them off lightly and then hose. Doing the underside of the leaves is probably of more use as that is harder to reach with sprays and probably a breeding ground. I've been trialling David Gray's systemic granules mixed into potting mix when I re-do them. Pretty toxic stuff though handle most carefully with gloves and a mask. (To steal someone else's line, if it can kill scale it can kill you.) Air circulation helps but really the ants can be a major problem in spreading this stuff. A bit of perseverance and you may well lick the problem forever and save the adults. Isolate the worst ones and they may well make more pups. Some Neos, some Aechmea and some Billgergias seem magnets, seems no problems with most Tills (even the ground ones) Vriesia or Nidularum. The fact that you have identified the problem early is half the battle won, I think. Good luck

Has anyone tried Confidor (imidacloprid) for flyspeck scale on broms? I have only one Aechmea with flyspeck scale and thought maybe a systemic chemical may work, but so far have not tried it myself.

If you use poisons, Rogor is really the best to kill the darn things with some wetting agent so it sticks.
Then a spray with soapy water every so often will keep them clean.
David Gray's is good for long term but the ANTS the darn things just seem to keep coming and bringing their friends with them.
Marion

A Condy's Crystals solution supposedly gets rid of ants from pots - would this have any adverse effect on the broms? (obviously one would have to ensure they put it into the pot, and not onto the broms).

When I find scale I use a maldison dip (same stuff in some dog-washes and KP-24). If you see Ants around your bromeliads it is a good indication of Scale, as ants farm scale to feed off the sugary secretions - treat the ants too. This will help keep the scale under control.
I have used confidor on other plants affected by scale and it works well, it should be good for broms too.
Do check that there isn't any little froggies in the cups when treating though.