I want to run a 20a circuit to a bathroom. My breaker panel is outside the house on brackets so I need to run the feed under the house. Can I drill through the floor joists and run to the room? Or do I run flexible conduit and hang from the floor joists?

Hmm this generally varies by area. You may want to contact someone familiar with your local codes; however, attaching conduit to the floor joists would probably be acceptable in most places. Since you are running the feed from an outdoor breakerbox, it sounds like you will have to use some conduit anyway.

Since the box is on the outside, you need weather and damage protection. NEC does not prohibit NMC or UF from running in conduit but it can be a pain to do so. I would run UF down the wall in NM conduit, make sure it is "sunlight protected", into the crawl space, then UF through the joists and up into the bath or all the way in NM condut and attach it to the bottom of the joist. UF is permitted in crawl spaces, NMC is not.

Thanks for the quick answers. I can either run conduit up the exterior wall to the attic space and across the ceiling joists to the bathroom? Or I can run it through the exterior wall into the floor joists then up to the bathroom? It's a house on a raised foundation and it's 1 story if that helps any more.

I would say do whatever is easier...

Under the house sound easier and a lot less wire. 12/2, 20 Amp, is getting near $1/ft. A lot of people now run 12/3 in the bath, 1 side to the GF and then pigtail into 2 leads, one for the light and one for the fan.

ma0641 the problem is when I start the run its outside and then must go through the stucco then under the house. I believe I need to have that exposed 12/3 in some type of conduit before it leaves the panel through the stucco. What do you suggest? Run a short feed to a junction box in conduit under the house and then splice 12/3 to the bathroom? Thanks you all the great help and ideas :-)

Sounds reasonable to me. If it's stucco over metal lath you shouldn't have too much trouble. Mount a junction box and I'd run 12/2 to the bath and then 12/3 from the wall up to the fixtures. There's no need to run 12/3 all the way, particularly with the cost differential. What is the cost in your area of UF 12/2 vs 12/3?