To confirm, you can call priority to reserve your monster's effect to the first chain.
so the chain looks like this:
Chain Link 1: Mobius, the Frost Monarch.
Chain Link 2: Bottomless Trap Hole.
Since chains resolve backwards... Bottomless resolves first and removes Mobius from play, but then Mobius's effect activates (since it's Chain Link 1) and you can destroy up to 2 Spell/Trap cards on the field.
Also, there's a difference between negate and destroy. Destroy simply "destroys" a card and sends it to the grave... But if you NEGATE a card, such as with Dark Bribe, it negates the effect (or makes the effect null and void) Mobius can't negate, so he can't save himself.
Even if he did negate, he wouldn't be able to since the only way he can use his effect in response to Bottomless is by calling priority, and by doing that, he wouldn't be able to "negate" Bottomless since it would resolve first, but just like in a real situation, you can still take out two other cards.
Also, please note that you must select Mobius's targets before Bottomless is chained. This mistake is usually made by the person with Bottomless because if you chain Bottomless without knowing your opponent's targets, then you can give your opponent an advantage. With three cards set, one of them being bottomless, if you don't activate, he may target bottomless, causing you to only lose one card, but if you were to chain bottomless instantly, it will give your opponent the initiative to select the two other spells/traps.
(In other words is Moebius still remains on the field 
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