Meeting a Geisha

I've been to the Gion Corner show before, but wonder if its possible to actually meet a Geisha in a more usual teahouse / restaurant setting.

I've heard if you stay at 5 star hotels the concierge can introduce you to a teahouse who could offer this - is this true, and is there another way of doing this without the 5 star guests. I've heard very expensive restaurants also offer this service - which would be better?

Also as I only speak very basic tourist Japanese, would I get any enjoyment out of it?

I briefly just google it:
http://www.gion-hayakawa.jp/ocha.html

Seems minimum usage is for 2 people, on side note: do not use the term geisha when you are in Japan, the correct term is Geiko, at least I read and heard the girls do not like the term Geisha there.

Hopefully someone with experience will share his experience here, I am rather interested with it too.

Oh and: http://www.japan-guide.com/e/e2102.html