Typically a bureau service will charge a small one-off set up fee and then simply charge on a per-card basis. The charge per card may be dependant on the volume of cards ordered per batch. A batch size could a single card or more.
The bureau service would set up a template for your card which might include your logo or other artwork that you may provide, a placeholder for a photo, name, designation, etc. You will be provided with a proof of this template for approval. Once approved, the same template will be used for all cards that you order on an ongoing basis. If you require a change to be made to the template (perhaps your logo changes), then you will be provided with a new proof for approval.
Thereafter, the ordering process typically entails emailing the provider with a photo of the recipient of the card and any other "personalised" data (name, etc) of the person. The bureau service will crop the photo and optimise it for contrast and brightness before printing the card. Cards are generally supplied within 3 working days of being ordered.
If you require large batches done at a time - perhaps over 20 cards - then the bureau service may request all data be provided in an Excel spreadsheet so that they can link to the data when printing cards. This ensures that data accuracy and printing efficiency.
If you require in excess of 10 cards per month, then you should consider purchasing your own printer as the total cost of ownership could be recouped in 12 months or less (depending on quantity printed and brand/model selected).