Your electronic devices are valuable, so you want to be sure that they won't accidentally break if they get splashed with water — that's what IP ratings are for.
Most manufacturers test their devices for Ingress Protection (IP) and the resulting rating (IPXY) is a measure of how hardy the unit is when it comes to dust and water.
The first digit refers to protection from solid materials, like dust and sand, and is represented by a number from 0 (no protection) to 6 (full protection). However, you'll often spot that the IP rating is shown just as X for this area — this shows the company hasn't actually tested it for protection.
The second digit is for water protection, and is the more common of the two. Phones, smartwatches, and headphones are usually tested for water resistance, ranging from no protection (0) to full waterproofing (8).
So, for bone conduction headphones, you'll want to make sure that they'll be able to withstand the environment you'll use them in. If you plan for some light indoor use to work out, an IPX4 rating for sweat resistance might do.
But for outdoor runs, where there's always the potential for rain, an IPX7 rating or above might be best. However, if they're exposed to more than the rating allows, that doesn't mean they'll immediately break, but it increases the risk.
Though because of the design, bone conduction headphones are often pretty durable and resistant to wet conditions. Unlike standard headphones, there are no audio drivers or speakers to get damaged, and all the electric components are stored inside the device.