Is it possible to kit or bundle an inventory item and a service together?

Yes. You can treat the service as an inventory item and then build composite items using Inventory -> Home -> Manage Build Orders.

You can also create an Item Option Group (Admin -> Inventory -> Item Option Groups) that contains services and assign the Option Group to the main purchasable item (General -> Additional -> Item Option Groups when editing items).  Services can then be selectable options to ordered items.