Note that you have to channel the area before building the bridge, because once a bridge is placed, you can't dig through the ground that it is on. You may want to channel part of your planned moat, build a temporary bridge, channel the rest, build your real bridge, then remove the temporary bridge so your dwarves don't get stuck either inside or outside after digging the channel. Also, don't channel something that's 3 tiles or more wide all at once, as your dwarves are pretty much guaranteed to get stuck (or cause a cave-in, but if you're not trying to dig your moat through your fort, that shouldn't happen) that way.
That is, where '.' is the ground, 'H' is the channel designation, and "_" has already been channeled...
.HHH.
.HHH.
.HHH.
.HHH.
.HHH.
This (above) is the bad way to make a moat.
...H. ..H_. .H__. .___.
...H. ..H_. .H__. .___.
...H. ..H_. .H__. .___.
...H. ..H_. .H__. .___.
...H. ..H_. .H__. .___.
You could channel as above, reading from left to right. Alternatively, you could do it this way:
..H.. .H_H. .___.
..H.. .H_H. .___.
..H.. .H_H. .___.
..H.. .H_H. .___.
..H.. .H_H. .___.
My point is that dwarves will find ANY excuse to get themselves trapped while doing their jobs, so only allow them to do it in a way where they can't possibly get trapped.
Actually, your moat doesn't need to be that wide, so I'm not really sure why I went on about channeling wider things up there. It (currently) would be just as effective if it were one tile wide, and you shouldn't have to worry about dwarves getting stuck when making such a moat. And finally, although it may not look as nice, a dry moat may actually be BETTER, because if it's filled with water, something that can swim can still cross it without any problems.