Similar bottles will sometimes come with a little red or black plastic cap that covers the tip of the bottle after it has been cut. If the bottles you bought didn't come with these caps, I don't know that there's a way to get them separately. Occasionally a restaurant supply store will let you switch out bottle tops when buying the bottles, but other than that, I think you may be out of luck.
Frequently to close up the bottles overnight or between uses, you take off the screw top with the spout, place plastic wrap over the top of the bottle, and then screw the top back on. As SAJ14SAJ points out, bottles like this aren't really intended for long term storage and caps generally aren't a priority.
Edited to add: The restaurant supply store nearest my house now sells the caps separately. They are in a package of about a dozen, but very cheap.