You have plenty of time to get it done before you leave and still time to prepare for school. Have everything ready before you start so the sinewing goes smoothly.
I'd put down two or three(if you have enough time)layers but one at a time. You can add the second a few days later or as soon as the first looks dry(big color change). You also have the perfect senerio as far as tolerating the wait of drying sinew.
Once you get the sinew on the bow place it in a dry spot with some air movement but be sure it is away from pets and pests. I let the sinew backed bows I make rest over the hot water heater in our utility room; out of sight, out of mind. You will have plenty to distract you between now and the time you get back home. The bow should be ready for final tillering then.