Hi there, welcome to BW
Sorry to see you didn't get a reply yet.
If you want to pat her tummy or hip (I kind of went for the hip/nappy area avoiding the tummy just in case it was uncomfortable) that's fine. Part of the shush/pat is the soothing rhythm and part is feeling/knowing you are there with her.
In the early days of shush/pat you can start in arms and continue until LO is fully asleep, when you put her into the crib you continue shush/pat for a full 20 minutes as this is the length of time it takes to get into a deep sleep. If you find this is not successful at all then you can continue in arms into deep sleep and then put her down and continue in the crib again, you may have more chance of getting her down and keeping her asleep if you do it this way for a while. Whilst this may not seem like a step towards independent sleep (because she is not falling to sleep in her crib but in arms) she will still be learning a great deal about the safety of her crib, her bond with you (that you are always there when needed), and will be making big steps in learning how to sleep feeling the weight of her little body on the mattress rather than the 'weightless' feeling of being held or in a sling. So it is still a step in the right direction.
Once you are able to put her down in this way you can begin to put her down a bit earlier, fully soothing with shush/pat in arms then going into the crib when her eyes are nodding - again continuing the shush/pat until she is in deep sleep.
If you observe her during this time you might see her doing the 'seven mile stare' - I discovered with mine he needed his 'stare' not to be interrupted, for this reason I needed to get him in the crib earlier so that his stare focus was uninterrupted and so that if he stirred during going to sleep (when eyes are nodding or if he woke again) he really needed to see the same view for his seven mile stare so that he could quickly relax again. Each time you change the way LO goes to sleep there will be a bit of a step back and some more soothing needed, it's a gradual process of reassurance and help to show your LO that she is safe and secure and is able to sleep alone.
For a LO this young if she is all out crying you do pick up. It is different to 'PUPD' used for older babies because you keep hold of her until she is fully calmed (PUPD for older babies is a more brief PU, they might be PD whilst still crying but the parent stays with them, they are not alone, it can involve lots of crying but never alone). At this young age there is no 'timing' to the PU, if she cries you pick up and sooth her in arms, when she is fully calm (or even asleep in the early days) you PD and continue to shush/pat and reassure in the crib to deep sleep. Shush/pat is not a magic wand and may well not sooth her instantly, it is a reassurance that she is not alone, the feel of your patting, the sound of your shush will become familiar to her as a sign she is being tended to and cared for. It can take a long time and it can be pretty hard work too. Although it might be hard work and your LO might cry several times during the process of putting down for her nap it is not at all the same as CIO. With CIO babies are left and do not know if mummy is ever returning. There is a big difference between a LO crying alone and crying with a parent, when you are there she might cry and she might be frustrated that you want to put her down, but she knows you are there, so she knows she is safe. The key with BW (as I'm sure you know) is to respond to your LOs cries, to go immediately to reassure, this builds the bond between you and gives her confidence. There may be times you feel like it makes no difference whether you are there or not because she continues to cry, but it does make a *huge* difference to her.
If you have the time/energy/patience to implement shush/pat in this gradual way for every nap you will see some results quite soon. If you do not feel you have the energy to do this for every nap other members of the community have found it helpful to 'work' on one nap per day in the crib and to sling nap for the other naps - if you decide to do this I recommend you do *the same* nap each day in the crib, for instance the first nap of the day. This is because babies build habits quite quickly, if the first nap is always in the crib LO will learn this and adapt more readily, if you chop and change which nap is in the crib it can be confusing.
I found BW when my DS was 4 wks old. Up until then I'd been using harvey karps 5s method to sooth and calm my LO (very similar to Tracy's 4s and a method other members have also used for very young LOs) and had already been gently attempting to put him down for at least some of his sleep. I introduced the EASY routine as soon as I discovered it and the combination of the 2 methods worked well together.
I hope this helps some. Don't be too hard on yourself, you are not doing anything wrong, it is just natural for your LO to prefer to be held the whole time.