Do the attacks only happen when you are trying to get her off her cage? Or is it when you offer her a treat from your fingers? Both?
If so, it sounds territorial to me. Is she young, around 7-15 months old? Or older and new to your home/this cage? (Or neither?)
Now, without knowing your full story this may be a shot in the dark but my advice is to get a nice play area for her set up outside and away from her cage and restart training her away from her cage.
If she attacks around her cage she's likely defending it and is trying to let you know she isn't falling for your bribes to lure her away. She probably knows what you expect her to do and feels pressured to do it, and is letting you know she isn't okay with that.
When my territorial lovebird went through this phase I ended up adapting ways to get her away from her cage without making her feel pressured. Instead of asking her to come to me I would sit nearby with a favorite treat and foot toys and wait for her to come to me. She could then make the choice on her own if she wanted to leave her cage or not and be rewarded with food, play, and attention once she did.
If she bites you when you offer the treat she may be guarding the treat too. Unfortunately this is something we can easily accidentally reward; if a bird bites our fingers while we are holding a treat, at least at first there is a good chance many people are startled into dropping the treat.
If you think the source of her aggression is food guarding, try offering it in different ways. For example, if you hold it pinched between fingers, what happens if you place it in your palm and keep your hand flat? If she still doesn't like that, I recommend keeping a cup or flat perch/surface nearby while training and just set the treat near her.
My lovebird will also guard any high-value treats and even 15 years later she will still eventually bite if I offer a specific treat 'wrong.' Some treats I can offer from pinched fingers, (bits of nuts, fruit) others I cannot pinch but she will accept from an open palm (millet, soaked pellets) others I dare not touch at all (nutriberries.)
It's a matter of learning your own bird's quirks and limits and unfortunately there is nothing that can be done to help that process beyond time spend together.
Also if she seems more aggressive of the straw at first than your own hands, why use it? I know a lot of sources recommend something like that for target training but if she's more comfortable with your hands just try pointing for now and acclimate her to the straw by leaving it nearby her play area so she can see and attack it on her own. Hopefully she'll get bored of it and let you use it again.