If you are unlucky enough to have buried underwater and dismounted, or are unable to get it back due to it being underground, you must use a transmitter to get it back, upload it then download. If it still is stuck, download at a supply crate.
Honestly don't use the bury feature while you are riding it. To use it press the jump button while riding it. The ability is cool and it makes you untargetable but if you are anywhere near water it will likely glitch and send you and your basilisk through the map and kill you both. I lost a level 100 in the upper mushroom One because of this. The Basilisk is fast enough and tabky enough to run away from anything without using the bury ability anyway. Thumb up so others don't lose one too.
This beautiful creature has a ton of carry weight, spits like a poison wyvern, can burrow underground and move while you ride it, and can slither over small obstacles. I want one. Just look out for them in your college’s sewer system.
When it is underground it does use stamina which means it can not be underground permanently, it is extremely fast when it is underground and untargetable, and when underground it will be blocked by structures such as, walls, foundations, rocks, etc.