Hello, welcome to BW forums

There is a difference between the BW methods and the No-Cry methods but the two work very well together. BW methods do involve some crying but you never leave your baby so cortisol levels are low and baby never feels abandoned (but likely frustrated by changes and will let you know that, in return you let her know she is safe and attended to) whilst the No-Cry or Gentle Removal Plan method avoids all crying (anything more than a little fuss) and moves much more slowly with the steps towards breaking habits and sleeping independently.
With the GRP if you are co-sleeping and nursing laying down in bed and want LO to move to a bassinet you would first make steps to stop the sucking before LO nods off and then when this is possible you would move LO further away from you in your bed so that you are sleeping at a greater distance with hands still on until she falls to sleep, then hands off when she falls to sleep. This would all come before moving her to the bassinet. I don't have personal experience of this but the steps make sense in theory... ...in practise though perhaps it is harder than it sounds. It seems that you are stuck at the first step with her either nodding off on the breast or crying again and being put back on the breast for more soothing.
You might choose to stop trying to put her in the bassinet for now (and fall asleep further away from you whilst co-sleeping) and take the steps more slowly.
Or
You could put her in the bassinet every time and get her used to it more quickly. If you do this I would suggest the bassinet being set up right next to your bed and you initially keep a hand on her either patting or gently rocking her body.
Either way, you might be able to replace the nipple with your finger which could help in getting her off the breast, or like Eva said try a paci.
There is a tip in the GRP to count how long you let LO suck for so that you keep reducing the amount of comfort sucking each time (this does not apply to nursing for hunger which is guided totally by LOs appetite), perhaps this would help you get out of this first step?
It's quite normal for LO to wake at the 45 min mark if there is a change to sleep habits because this is the end of a sleep cycle and instead of just half waking, being reassured by your presence and returning to sleep, LO half wakes, realises things are different and so fully wakes to find out what's wrong, what's changed? Where is Mummy? If you keep a hand on her throughout sleep you may be able to reassure her through that sleep cycle transition into the next cycle and teach her she is still safe. This is the basis of the BW methods which are to teach LO that you will always be there when needed and in fact LO then needs you less, their confidence and trust in you remains in place.
I'm having trouble with the server just now so can't link our GRP thread for you. It's a useful link that has lots of mini-steps to follow and you can adapt it to what suits your current situation. You can find it in the FAQs on Sleep. I have read Pantely's book but to be honest I can't remember if our FAQ extends or just repeats what is in the book. You may be able to find the link yourself, I'll try to come back to link it for you too.