Unfortunately, there really aren't - at least not in the US - can't speak for other countries. The grants that help start businesses are mostly for technology and energy - Arts grants are almost all program based - as in there are funds to bring arts to underprivileged children or to special needs kids but not to open a business. Also, almost all arts grants go to established non-profits like large ballet companies or inner city programs since you have to have a long track record to win the grant.
Your best bet in getting an art grant is to approach a non-profit that is already doing something - like taking extra-curricular programs to impoverished schools - and offer to write the grant application for them. These organizations are short staffed, they qualify for the grants but they don't have enough people to write them so if you can pitch a dance program to them they may help you locate the grant if you are willing to do the writing. Then, if they are awarded the grant, they 'hire' you to teach the class and the grant pays your salary.
The other popular type of art grant that applies to dance is for performances - the National Endowment for the Arts gives hundreds of thousands every year to help people stage productions but again, they generally go to established companies and universities. For example, American Ballet Theatre is awarded something almost every year so they can stage new choreography or a famous work.
Arts grants are very specific and they can vary a LOT by area and the chances of you finding one to open a studio are non-existent. I don't mean to burst your bubble, really I don't, but its a wild goose chase... sorry.
If you want to attach yourself to a non-profit and look for grants that will 'employ' you as a teacher/choreographer here are the places to start - also these sites have great information for a business plan if you're writing one for a studio... good luck!
www.artsusa.org
www.nea.gov
also, google 'your state name' arts council and you should find your state level office of the National Endowment for the Arts - almost all there grants go through the state offices anyway.