There is no such thing in D&D 5e as "physical" damage. Damage reduces your hit points and comes in a variety of types but there is no mechanical difference between say bludgeoning and psychic damage - both cause loss of hit points.

"damage from spells" needs to be given a simple reading. Damage from a spell is the damage that is listed in the spell's description- that is the damage from the spell. Specifically, the damage from Bones of the Earth is damage from spells.

Examples of things that are not damage from spells is the damage done by summoned creatures, the damage done by a polymorphed creature or the damage done by teleporting someone 3 miles above the earth and letting them fall. This is because none of these sources of damage come from the spell description.

Rules as Intended: No

Jeremy Crawford has clarified:

Q: Is warding bond the source of its generated damage instance? If so what damage type is it? Is it still spell damage? thanks

A: When you take damage via warding bond, you're taking damage from whatever caused damage to the target of warding bond.

So, according to Jeremy's clarification, the damage you receive from warding bond is considered the same source as what damaged the ward. Thus, the only time aura of warding would work on it is if that original damage was caused by a spell.

As always, it is up to the DM to decide how much designer clarifications and intent means at their table.