I used to put two bottles in the cage for a while as I was worried about our hammy getting water out. Then if one fails they can use the other one. I found them a total pain - I had some that wouldn't let water out very well and some that leaked all over. I ended up using the 75ml mouse sized bottles that Souffle mentioned. The classic ones are popular but I found the best ones were the Ferplast drinky (not sippy) which have a slightly bigger metal spout. They always seemed to let water out and never leaked or dripped everywhere. They also come with a neat little clip for bars so the bottle can be on the inside of the cage rather than the spout going through the bars (our hammy hated the spout going in and out of the bars!).
If you've tested it with your finger and water is coming out then it should be ok, but I would have a second bottle in just in case. Sometimes they do bite at the metal spout - I think they get frustrated that it doesn't let water out quicker.
There are a couple of tips I've picked up on here that might help as well. One is to not completely fill the bottle (eg fill it about 3/4 full). The air gap somehow helps the pressure of the water so it comes out easier. The other was to try different things with the tightness of screwing on the lid. Leaving it very slightly unscrewed allows the water to flow a bit free-er. But too loose and it can empty itself (hence it's good to have a second bottle!).
Are you in the Uk? These are the bottles mentioned
Fpi 4660 Drinky75 Drinky B.
I had the bottle the other way round in the clip - easy for changing the water. The clip stays on the cage and you just lift the bottle out and replace it. Getting two saves on extra postage (you only pay one lot of postage). As well as a second bottle it's always good to have a spare in case one stops working.
Crystal Deluxe Mouse Bottle 75ml
You are doing the right thing tapping the end with your finger - I think that is needed every day. You don't really see the level go down because they don't drink that much so it's not really noticeable.
Our hamster wouldn't use a dish - if you do try one it needs to be very shallow or they can fall in them and drown or get wet and it's bad for hamsters getting wet. Placing it can be difficult too - on the substrate it can get substrate and food in it easily and get bacteria. On a shelf or house roof this won't happen so much but they can knock it off, or push it off. I'd go with have two small bottles
