Ok, i've done more searching and it seems that this is a common problem in rarely used drains. Apparently the "solution"is to ensure that there's water in the trap (I don't think my idea of a "deeper" trap is a good once since that will likely cause slow draining). We've never had this problem before, so I'm not sure what's different now.

One other possible culprit is that "gunk" is caught in the stopper mechanism (hair, etc.) That's impossible here since the bathroom is used only for handwashing now and then. Nothing but soap and water goes down there (I'm the only one who uses it).

I have the same problem with my upstairs bath, which comes and goes (the smell problem, not the bath :). I noticed a sewery smell comes out of there during the first few minutes of running water. I was envisioning some gas bubble that gets dislodged when water goes through the trap.

I finally asked a plumber about this. He said that the smell is, indeed, caused by "gunk". Namely, the gunk that collects inside the sink itself - i.e. the space between the slot that prevents the sink from overflowing and where it joins the pipe just below the drain opening.
It's almost impossible to clean in there, but he said you could try to use bleach and pipe cleaners.

The gas bubble idea still makes more sense to me, but I guess he's seen his share of gunked-up sinks.

"the space between the slot that prevents the sink from overflowing and where it joins the pipe just below the drain opening."

Do you mean the open holes on the side of the sink opposite the faucet? This sink has never overflowed (or even close), so I'm not sure how anything could get in there. But, I'll certainly check it out. Pouring bleach and cleaners down the drain was, well, money down the drain (sorry, couldn't resist).

Thanks for the tips...

It's also possible your vent is plugged. located inside the wall a vent pipe allows sewer gases to pass to the outside. if leaves or some small critter gets into the pipe the venting will stop and next place the sewer gases will come out at is the plumbing fixture.

garden guy - I thought of a plugged vent, but if this was the cause, then I may be receiving the same smell on other fixtures on the same vent, but I didn't.

After some inquiring, it appears that some milk may have spilled in the overflow (kids!). So, I poured some bleach down there and it appears to be working...

That's good. I never would have thought of the roof vent being blocked, but, as you say, if there's a lot of wind it can suck some of the water out of the u-bend giving the gases the opportunity to go back up the pipe...why one bathroom and not another? Gravity and position relative to the sewer I suspect, one'll be affected before the other.

Apart from kids pouring things where they don't belong (little darlings) just make sure you run the water now and then, to freshen up what's in the trap.