Like Geekmom said, it could hours or days. It isn't just a "Bam!" And then baby comes like on TV. It's a long process. Some people don't realize when they are in early labor and things seem to go faster for them. However, you'll still have time to dress.
I labored at home for 12 hours before going in to the birthing center. It took that long to go from SROM and the first contractions to get to the point where I was contracting steady at less than 5 minutes apart and ready to go in. I took a shower, talked on the phone with my midwives who told me not to rush anywhere yet even though my water had broken, packed my bags, washed some dishes, watched TV, hung out with my husband and my mom... it was a long day but it was super comfortable to be in my own space on my own schedule. No need to run to be seen immediately.
You can be the latent phase for days so as abive said waiting for contractiobs to get closer together and more intense usually gives you time to get a few things done. My mum said with one of my siblings she went shopping because she suddenly realised she didn't have any food in the house for when she got home. With another one she decided to finish painting the nursery before going in.
It depends on how fast labor progresses. You normally don't go to the hospital until they are about 5 minutes apart or so, and you won't be pushing until about 2 so if you get them and are only at 10, you will have time to stay home for a bit and shower and whatnot. At that stage, they shouldn't be too bad so you should be fine.