There are several ways to do this better.
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As you said, you can hold it til they try to make a move and have an easier time landing it, since you know where they're going.
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You can use your E on yourself to slow them with your autos, making them easier to hit. (This way I'm going to talk about a bit more in a sec)
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Practice. You're going to need to practice more anyway, so this one will net you the most worth.
I'm a Lv7 Nami, so pretty much, I'd say the reason you're not doing well is more than likely because her bubble actually travels somewhat slowly. When you're looking to hit someone, try to imagine where they're going to be after about 1s. It wont account for flash/escapes, but if they used summoners or cooldowns to dodge you, then you're still technically doing your job and making a lot of pressure. If they're the aggressors, it's easier since they're trying to push damage onto you. If you're trying to make a catch, try to get yourself to a point you can throw it slightly behind them. They'll either have to stop and take some poke damage (still did your job) or they'll have to use an escape or summoner to not get caught.
When is she good? Tbh she's pretty good in general. About the only time I don't like playing her is against Lucian, since he's pretty much impossible to peel. Ezreal's annoying and you likely won't catch him, but I wouldn't say it's a bad matchup. Lucian's just a constantly in-your-face champion that's gonna dash every time you use Q and chunk you and your adc all day.
Until you know how to land your bubbles...there's another way. It's something I came up with when I was trying to make a build capable of solo laning it in mid.
Hail of Blades/Taste of Blood/Ghost Poro/Ultimate Hunter||Font of Life/Revitalize
This is what I was talking about when I said I'd talk more about point 2 in a sec: this setup puts more emphasis on your E than on landing your bubble. It's more aggressive, so you won't heal for as much as the usual Aery page, but you can still give additional access to healing through Font of Life if your adc is committing with you. This is not a standard way to play Nami, but it will help you until you feel comfortable landing her bubble and playing more around it. It also starts you on the more shallow end of the bubble timing, since they're going to be significantly slowed when you try to land your bubbles. If you use this setup, start with E/W/Q instead of W/Q/E and max E/W/Q instead of W/E/Q to maximize its output.
You'll learn eventually how to hit them on targets moving at normal speeds, and also on people like Udyr or Yi who have stupid amounts of it. For now, if you want to try this method, it may fit you a bit better than playing full support for now. Once you feel comfortable, switch back to the more standard support page.
Aery/Manaflow/Transcendence/Scorch||Font/Revitalize
I personally like to trade out Font/Revi for Cheap Shot/Ultimate Hunter, but that's because I play super aggressively.