Make it 3 for no salt.
Trees are very persistent critters. We have a lot, ok, mostly clay and rock. Anytime I put in a new bed, I just resign myself to the fact that the trees are going to find it. I've had roots come to the top of a 18" deep bed because it was rich soil.
That said, if you have a way of sealing the bottom of your beds, go ahead and do that. Once that is done, you will need to address the drainage issue. Drill some strategically placed holes about an inch above the grass line. You can run a piece of PVC pipe through it, or even a piece of old hose. Either will work to keep the hole open. Don't make the hole too big, or you'll have 4-legged critters setting up housekeeping.
The next time you're out and about, if you see a brick or block retaining wall, look along the bottom. You will most likely see a number of these drainage or 'weep' holes. For retaining walls, they're put in to relieve the pressure from excess water build up. In your case, you want any excess water to be able to drain out.
BTW, for 'running' varieties of bamboo, as opposed to clumping, I believe you have to put a non-permeable barrier down at least 6 feet to keep the bamboo in check. Sorry, but that's just too much work. Then again, tearing out our bamboo patch was no easy feat either. It took me a good 10 years one summer to get it all out!
