Hello PeculiarLocks,
You do not need to connect your Monzo account. If you are using QuickBooks Online however you will need to create that Monzo account as a Chart of Account to record the expense against. To do this, go to Accounting > Chart of Accounts > New, select Cash at bank and in hand as the account type, and Current as the detail type then name this whatever you would like. Then, whenever you're recording a transaction you used your Monzo account for, select this under 'Payment account'. This will make sure QuickBooks does not incorrectly deduct your business account by the expense amount when it was not that account that you used.
If you are using QuickBooks Self Employed then you can manually add the expense in the transactions section. Or you can upload a CSV file of the transactions into QuickBooks. You can also snap expense receipts and add them into QuickBooks.
You only need to record transactions relating to your business. In regards to your owner's withdrawal, this would be something you would need to check with an accountant or HMRC. It is up to them if they think it is important for you to record what you spend this amount on - however this would only be important if you are using this money for business expenses.
Please let us know if you have any further questions.
Thanks,
Talia
