1. are filters hooked up properly - i.e., water is flowing into the "gozinta" end and coming out of the "gozouta" end?
2. air needs to be able to escape from the bottles. they can't be sealed tight with the only opening having water coming in. obviously, pressure will build up in this case.
3. cap can't be on the supply/unfiltered water bag. air must be able to enter the bag as water flows out.
4. also, hang bag high. obviously, again, it should not be near the level of the bottle that you are filling.
sorry, i know that these are the most obvious reasons (based upon my understanding of your description) and you've probably already thought of these.
here's a troubleshooting tip - in one word: SIMPLIFY (the system). since you're testing it, remove all of the filters, and any other unecessary parts of the system, leaving the fewest components possible to have water flow from the bag into the bottle. try to fill the bottle a couple of times. note flow rate & time how long it takes to fill the bottle. obviously, if flow is NG in this "simplified" system, then you've got a problem with you water supply bag or tubing. blow air through them and see how air flows. now add one component back into the system. repeat the test noting flow rate & time to fill the bottle. continue until you have identified the "culprit".
hope someone else can be more help to you.