CE marking of device that contains CE certified module
What applies here is the Radio Equipment Directive (RED) 2014/53/EU. This in turn points at a whole lot of technical standards, as well as requirements from the Low Voltage Directive (LVD) regarding electrical safety. How much of it that applies in your case depends on the product. If I remember correctly, the relevant standard for Bluetooth devices is ETSI/EN 300 328. This standard should be available for free from ETSI.

If you don't change anything that will affect the radio characteristics of the product, then you shouldn't have to do any additional radio testing. Meaning for example that you must use one of the antennas that the manufacturer of the Bluetooth modules have used during their tests. This should also mean that you don't have to redo the tests for Bluetooth compliance - this isn't required by EU, but by the Bluetooth SIG.

However, you will have electronics surrounding the product, including a voltage regulator that provides supply voltage to the radio. These electronics need to conform to the EMC directive and you need to be sure that they don't affect the radio. That's the advantage of doing a formal radio test at a test house: you get EMC tests included, as EMC for devices containing radio is a special case where the RED directive overrides the EMC directive.

You need to write an EC declaration of conformity where your company vouches that the product fulfils the requirements of the RED directive. You can then chose different ways of ensuring that this is the case (set out in RED Article 17), including internal control or by using a test house ("notified body").