The bell does actually help, but it's not as reliable as a lot of people think - some cats just don't slow down with it, and the birds get used to it too. You could still give it a try, but don't expect miracles. What's often more effective is a combination approach: for one thing, you should limit her hunting times, so bring the cat inside in the mornings and at dusk (when birds are most active). For another, there are special vests or harnesses that restrict movement - not meant to be cruel, but they do reduce her jumping power.
I've also heard that some people put nets over certain areas in the garden or plant dense bushes where birds land. That basically cuts down on "hunting opportunities." And honestly, if your cat is really obsessive - some are just too successful as hunters - you have to accept that outdoor cats do hunt. That's not mean-spirited, but it's just their nature.
Keeping her inside completely probably isn't practical if she's not used to it. But a compromise might be to only let her out at certain times, or build a large outdoor enclosure if you have the space. That way you can keep her active without locking her up completely.