How to seal a hole in a plastic bottle properly?
PETE is hard to bond to.  It does contract if you melt it, so here's an experiment to try (it may take several attempts to get the feel of how the plastic behaves at the melting point, but at least for the bottles, you have an endless supply):

In the area of the tube that will be next to the bottle wall, wrap a strip cut from another bottle many times tightly around the tube (the layers directly on top of each other), and hold it in place temporarily by wrapping a piece of wire around it or using a soldering iron to melt the end to the next layer.  Melt the windings with a heat gun until the layers flow together into a solid collar and let it cool.  See if it becomes mechanically tight enough that you would expect it to be water tight (if it can't be moved).  

If so, slide the tube into the bottle from the inside so the collar is against the bottle.  Wrap another strip around the tube on the outside, against the bottle, and repeat the process.  Use the heat conducted by the tube to remelt the first collar and the wall of the bottle to fuse everything together, but not so much that it falls apart.  

If you can't pass the tube through from the inside of the bottle, try this just fusing the wall of the bottle to the first collar on the outside.  You can experiment with adding a PETE washer cut from another bottle on the inside to provide additional wall material in the melting area.  It also might help to stick a metal washer on the tube on inside, against the wall, to help evenly heat the wall material to fuse it to the collar.  If the bottle's neck is still in place, working on the inside may not be practical, but you could still add the PETE washer on the outside for extra wall material.
If the first approach doesn't pan out, I would stick the tube through the bottle and seal it on the inside like this (if the bottle's neck is still in place and you can't access the wall inside at the tube, you could do this on the outside, but it wouldn't be nearly as effective):

Put a fairly thick band of silicone rubber (RTV or silicone caulk), on the bottle wall around the tube, getting it onto the tube.  Put a loose-fitting metal washer on the tube and press it against the rubber, hard enough to spread the silicone flat behind the washer and squeeze a little rim of silicone out around the washer's edge.  Silicone should also fill the washer's hole around the tube.  Add a little more silicone to seal the tube to the washer.

If you do this on the inside, any pressure will enhance the seal.  If you have to do it on the outside, you're relying on the bond between the silicone and the PETE, and that may not be great, especially if the tube might be moved.
Still another approach is to not use the bottle's wall; use the cap, instead.  You can pass the tube through the cap (or even multiple things through the cap, and then orient them as needed inside the bottle.  The cap seals water- (and pressure-) tight.  If the bottle is vertical, you may not even need to worry about how water-tight the tube is in the cap.  Otherwise, use silicone rubber to seal the tube to the cap on the inside of the cap (so any pressure enhances the seal).

If you also need mechanical strain relief, the plastic caps can be welded together by fusing them with heat.  Weld two caps back to back and drill through the joined tops for the tubing and whatever else.  One cap gets sealed with silicone as described above and is screwed onto the bottle.  The other cap can be filled with hot-melt glue or epoxy to provide mechanical support to the tube.