This happened to me at 33 weeks - for a moment I just stared at the tiny white drops blankly wondering what on earth they could be. I have to say that once I got over the surprise I find I rather like having such visible proof that my body's getting ready to feed my baby from the outside!
I was still feeding dd until about 20 weeks and having toddler milk on one side and colostrum on the other was very odd Lots of things weird me out about being pregnant though, especially thinking an entire person is happily swimming around in my belly!
Mine comes out at night because I'm squishing my boobs lying on my side, I woke up to find my boob stuck to the sheet in a patch of colostrum, so weird! I find little marks on the sheet a lot. Only been awake to see it dribbling out once. I keep pointing it out to DH because I think it's so clever of my boobs to do it!
I think it's the heat of the bath that does it. Mine started at 29 weeks but I was in Italy in 30+ degree heat. I just noticed a small wet patch on my top at night which carried on throughout the holiday. In the bath it poured out! But now back in the UK and haven't seen much. Only in one boob though - weird!