Okay, so here are my thoughts on this. When you're going over and taking her paw and ringing the bell, I don't believe you're training her to ring the bell like you believe you are. You're physically doing it for her. I believe, in her mind, she's just tolerating it, because it's something you make her do before a walk. The same way you trim her claws or bathe her. It's just something she has to tolerate before a walk.
Instead, you want to get her engaged with the act of ringing the bell. All dogs are very good at recognizing patterns that lead to behaviors. In fact, people often think dogs initiate a behavior to get a reward, but often they're reading a humans body language and they are preforming an action because they know it's coming, not because they're actively trying to generate it.
The way I'd approach this is to think about it like she does. Try to go through it in your head like it's a foreign language. Actually, it's hard for people to do, because we are so language oriented, but try to go through it without thinking the language in your head. To people, we visualize the bell and think "okay, there's the bell", "dog rings bell, I open door". The problem is that people are good at context and abstraction and most animals aren't.
Instead, it's like if someone started giving you a weird hand sign they made up and when you looked at them like they're stupid, they tell you it's supposed to mean, sit in that chair and I'll give you $20 bucks. You have no idea what it means. However, if they give you $5 every time you get within 10 feet of them, you'll start coming around them all the time. Then if they give you a $10 every time you sit on anything, you'll start siting on everything you can. Lastly, they'll go stand near the chair they want you in and when you sit like you've been sitting on everything, they'll give you a $20. You'll start wearing that chair out. Once they know you're going to do it, they'll add their weird hand sign in. It may still be weird to you at first, but pretty soon, they'll make the sign and you'll just walk over and plop down in the chair for your $20, because who couldn't use an extra $20 for so little effort. However, this time they give you a jackpot reward of $100. You'll come from another room for a $100.
It's the same principle with the dog. I'd start by holding the bell out and letting her sniff it. When she does, I'd either click-and-treat (see internet for more info) or tell her "Yes" and take her out. Once she knows to touch it with her nose, and I mean even a quick sniff, set it on the floor near the door when you're ready to take her out. See if she'll sniff it. If she doesn't, then back up and hold it up for her or put your finger near it. When she sniffs it, reward and go out. After she knows that she goes out when she touches it, repeat for a week or so. When it's habit, let her sniff it and then don't let her out. When she sniffs it again, then let her out. What's happening here is that she knows sniffing it gets a reward, but this time it didn't so she tries to do it with more authority. Click-and-treat, being food based, can really ramp up the motivation here. Especially if the weather is nasty outside. The goal is to get her to hit it repeatedly and start to hit it harder from mild frustration. Eventually she'll cause it to ring and you'll jackpot her with lots of praise and treats, so have them on hand at all times to jackpot any ringing of the bell. Good luck.