LOL! Very true!

If Dumbledores gay then so could be River

She could be but it would be a shame as she's HOT! (sorry i'm terribly hetero-oriented - guess thats a fault nowadays but oh, well.....) ;)

Could be she's a bit gun-shy around men due to her experiences at the Academy too . . .

This hypothesis has crossed my mind as well because Joss doesn't object to gay characters, and River's sexual orientation has never been fully fleshed out. However, (for me) there is little evidence to prove either argument.

If you want someone to play devil's advocate, I'll play.

She LOVES to provoke Jayne. She teases him when she can as if she wants to pull his hair and run away, metaphorically speaking. And, she's never been afraid of him: "Jayne is a girl's name./Also, I can kill you wit my brain" (both quotes from "Trash"). And in "Objects in Space", the "object" she had in her hand in the beginning was Jayne's gun that she got from his bunk. She could have gotten anything from any place on the boat, but she ended up wandering into his personal space.

And, she's grown very close to Mal, especially at the end of the BDM. Both of them have lost nearly everything but their lives at one point or another. Throughout the entire film, there are a lot of fades and scene cuts from River to Mal and vice versa. For example, on the cross-fade on Kaylee's line in the cargo bay, "... just like Simon and River. Just like Inara," Mal and River's faces are placed to resemble a yin-yang.

*reads over what was written before officially posting* Boy, I've been studying film rhetoric too long. This sounds like a paper. LOL!

The word you're looking for, I reckon, is 'subjective'. :)

What can I say? Innocence != gay. I'd make the opposite case: without the possibility of things getting sexual, River is more comfortable around women. Meaning she's straight. :)