Do not get hung up on "bonding" - the baby will know where to turn for this.
I think that you seem most irritated by the fact that your Mum thinks you will not manage without her - it would get up my nose too.
It is swings and roundabouts. Having someone there who will cook, wash clothes, clean etc. is a godsend; but having someone there who takes over with the baby is a total pain. Your Mum needs to know her role - the baby is your (and your OH's role) - and hers is just to support in the background.
It is hard having a first baby and there are times when you feel uncertain and insecure and you need to be able to share that with your OH, rather than having "Supermum" breathing down your necks. If your Mum is there, it is very tempting to give in to those moments of insecurity and let her take over.
Tell her you are grateful for her offer and it would be lovely to see her for a couple of days when your OH has to return to work.
The problem here seems to be that she does not know her place!
When my last GC was born, I went round to DDs and the house was rammed with people. I stayed for about an hour and said that I would pop off now and let her get some rest, but be on the end of a phone if needed. She actually begged me to stay, to my amazement! - I think she was just inundated with in-laws and wanted one of her own there. I settled down on the bed beside her for a short while and just chatted a bit - it seemed to be what was needed.
But, without patting myself on the back too much, I think we knew our place and were happy to tread softly and recognise who the parents were - not us! I would just roll up with a meal then leave with the washing!
Perhaps you could try and make a list of those things your Mum could do that would be most helpful to you: food, washing, shopping etc. and present her with that - maybe she will get the message! She is going to be excited for you both, but needs to stand back a bit.
I would have gone apeshit if my Mum had barged in and taken over!!!