and how many do you think would fit fairly close together in a 30" (?) circle? My geometry skills are long gone!

Wendy, yours winters starts earlier and are colder than mine, so your experience could be completely different, but let me give you the scoop on my experiments.
I don't have a w/barrells, but do have two fairly large pots comparable in size to w/b .
Winter before the last I planted both of them with all kind of leftover +late season sale bulbs. There were crocuses, hyacinths, daffs and all kind of tulips, from early to late one.
By pure accident one of the pots ended up for the winter in a cold frame where it was not watered the whole winter except ocassional shovel of snow, another was left outside being exposed to all rains and snow.
In a spring crocuses in both pots sprouted and bloomed at the same time. Hyacinths in a 'cold frame' pot were little bid earlier than in an 'open pot'. Daffs sprouted and bloomed at about same time in both pots, but tulips in 'open pot' ALL become a mush while 'cold frame' ones sprouted and bloomed at the same time as those that were planted in a ground.
My take on this is that tulips are much more succeptible to rot than any other bulbs due to our wet winters and constant freeze and thaw cycles.
Nevertheless, I think that your idea have a merits if you will come up with some cover for your w/b to avoid excessive water/melting snow go into it. I guess simple plastic will do it.
IMO, Triumph tulips should be good for experiment.
They are annuals anyway, bloom mid season and tall enough (14-18"). As to quantities, I think for 30" barrell 25 planted close enough in a center should produce a nice display.
Good luck and post a picture!

Thanks George! That's very interesting. I tried a similar experiment last year with some pots in my unheated garage and some outside protected. But I can't remember the results!!!!!!

Sounds like some HD value bags would be a good way to go. I can try layering too to extend the show. Maybe some daffs and hyacinths for early followed by tulips.

http://www.gardenforever.com/pages/artLayering.htm

for covering, I could put a rebar in the middle and make a "roof" with a sheet of vented plastic tee-pee shaped to keep the snow off it. maybe one good fall watering before covering it up.

A very interesting experiment. I also like the idea of layering the bulbs among perennials. So far I have only included some alliums with the groups of tulips I planted. But I bought so many tulips they took up every inch of space between my perennials. It would be difficult to stick a wire in the ground without hitting a tulip bulb. No space to plant any other bulb at all. The bed is not very big, anyway, so layering seems a perfect solution. Also for the whiskey barrel, I think, because it would be in flower longer.