New puppy mummy

Welcome
Congrats on your new puppy!

 

Teaching independence is really important.

Its a good idea to prepare for this as early as you can - get her used to you walking out of the room then immediately back in again, preferably when she is occupied with something like a Kong. Try to make no fuss, you don't want to prepare her into thinking "oh no this means they are going out" - the aim is for her to barely register you coming and going - ideally for her to have a 'oh, you're back, I didn't notice you leave' reaction. Very, very gradually build up time. This will be hard work but put the work in now and it will pay off later. If she gets distressed though you have gone too fast, and created anxiety and that is not what you want. Stair gates are also useful to allow her to see you pottering about in another room, but without being glued to your feet.
You can also reward independent behaviour - praise when your dog is not actively engaged with you, which is actually quite hard to remember to do because we sort of don't notice when it happens!

There are other things you can do like picking up keys and putting on outdoor clothes then not actually going out, to desensitise her to the triggers that signal you leaving.

An Adaptil diffuser releases calming hormones in the house and might also help.

@JudyN has written some great stuff on this.

 

Good advice from Joanne.
Also remember to not over coddle her. If she is constantly resting on your lap or touching you in any way she will become over dependent on your scent. If this has happened already the try the Adaptil and add in an old t shirt or similar that smells of your recent scent.
Are you crate training? Some dogs find crates (better described as "dens") very comforting.

 

Sleeping on your bed, lovely though it is, does not help her to learn to be independent. She is surrounded by your scent and when you take your scent away (go out) she cannot cope. It is very distressing for her and her behaviour not deliberate at all.
I would wean her, gradually, off your bed. Pop her in a den or puppy play pen beside your bed so that you can dangle your hand down if she gets distressed. Once she settles there for a few nights gradually move the pen away from the bed a little bit every couple of nights. Once she is near the door put her outside the door but leave it open. You are aiming, eventually, to have her sleeping outside the bedroom completely. This will hugely increase her confidence in her ability to cope without you being right next to her.

Use barriers like stair gates etc, to confine her, with lots of lovely chew toys, stuffed kongs etc for short periods each day. Do not allow her into the loo! You are not being mean you are helping her to be happy! Separation Distress is a terrible thing for a dog to suffer from.

There are other techniques to help her but none of them are going to work until she has learned to be more confident in her ability to cope on her own. It is a bit like children going to school they do have to learn to cope without their mum!