As a rough estimate, the cost is $10k-20k, plus your labor cost.
In the US, all products containing electronics that oscillate above 9 kHz must be certified. The law that governs this is FCC Part 15. The lawyers call this "Title 47 CFR Part 15," meaning that it is the 15th subsection of the 47th section of the Code of Federal Regulations. In Europe, there is a similar regulation called CISPR 22. The requirements are almost the same, but slightly stricter about emissions at certain frequencies.
You can read 47 CFR 15 online. It's not as incomprehensible as you might expect. It seems overwhelming, but if you read the first few PDF's, you'll realize that most of it irrelevant for any single product.
Within 47 CFR 15, there are two classes of testing: Class A and Class B. Class A is an easier test to pass, intended for devices that are used in industrial settings. Class B is stricter, intended for devices that are targeted at consumers.
There is additional testing for "intentional radiators," meaning radios, Wi-fi, Bluetooth and such. There may be an exception if your device is intended for use as a component in a larger system (like a microprocessor or memory card in a PC), but I'm not sure of the legal details there.
The major expense is renting the test chamber. This is what's called an "anechoic chamber," instrumented with a pile of sensors for detecting electromagnetic radiation. To my knowledge, these cost around $1000/hour, and each testing session takes 2 or 3 hours. It's unlikely, but not impossible, that you will pass on the first try.
Here's a decent picture of a test chamber. The one I've been in was actually much larger, like a squash court. I think it was an Intertek facility in Menlo Park, CA.
Unless you're experienced with emissions testing, it is worth hiring an expert, which costs around $500/hour. They can tell you things like, "Put a ferrite bead on that power cable, and that will reduce the emissions at this frequency." The folks I've worked with arrive with a bunch of ferrite beads and inductors (and maybe caps?) of various sizes that you can use in the chamber to hack your device into compliance.
(Perhaps it goes without saying, but I'm an engineer, not a lawyer. I have taken a few products through Part 15, but not in the last couple of years.)
If you're thinking about doing this, start by reading EMC for Product Designers by Tim Williams. I'd avoid the books by Mark I. Montrose; I found them less helpful and more expensive.
If the device is deemed to be information technology equipment (which it may, since it uses Bluetooth) you would be under the '60950' standard - UL 60950, and if you want to cross the border into Canada, CSA C22.2 #60950 (the standards are largely identical, so it makes sense to get both).
Intertek ETL is a US Nationally Recognized Testing Laboratory (NRTL) authorized to test to UL 60950. You could use UL, CSA, TUV, MET or any other NRTL to do the approval - it doesn't have to be Intertek.
The best way to know if the product needs approval is to get an opinion/quotation from an NRTL - they'll tell you what they believe the product needs and how much a certification will cost.
Best Answer
You are confusing certification and emissions requirements. Only intentional radiators need to be certified. From your description, your device is not a intentional radiator.
However, you are still obligated to ensure it does not radiate excessively. The limits are defined in part 15 of the FCC rules.
How you determine for yourself and ensure that the device does not radiate more than allowed is up to you. The FCC doesn't go looking at the millions of devices that are unintentional radiators and test them for compliance. However, your competitors might. If they find your device radiates illegally, they can file a complaint with the FCC.
The worst case is if some communication got interfered with, the FCC investigates, and finds one of your devices causing the problem. Then it gets serious fast.
Large resellers may require a recognized lab to certify that your device radiates legally, or they won't carry it.
All that said, for a little guy selling a few 100 gizmos a year off some web site, there is very little chance anyone is going to check whether the device radiates within the limits. If you follow best practices, like a good overall grounding strategy, filtering of external wires, etc, chances are very low your device will radiate enough past the limits for anyone to notice or to care.
As Dirty Harry would say: "you've got to ask yourself one question: 'Do I feel lucky?' Well, do ya, punk?"