Bill can be used to document the cost of any service or product, but in actual conversation we normally use bill for simple transactions. At a restaurant you pay the bill after you finish eating, or you might get a bill for services when you bring your car in for an oil change.
For more complicated transactions, particularly in business, the more common term is invoice.
invoice (n): A list of goods sent or services provided, with a statement of the sum due for these; a bill.
We will prepare an invoice and send it to you as soon as it's ready.
This can sound more professional, especially in a business environment where the service is complicated enough to require listing the details. By definition the invoice contains all the details of the transaction, so unless there is some contextual need, you shouldn't have to explicitly say it includes details.
Note that invoice can also be used as a verb, meaning "to send an invoice to someone".
We will invoice you as soon as we [have/write up/put together/etc.] all the details.