You can teleport, but it may not block the damage
Emboldening Bond states:
Starting at 1st level, you can forge an empowering bond among people who are at peace with one another. As an action, you choose a number of willing creatures within 30 feet of you (this can include yourself) equal to your proficiency bonus
I'll assume the two creatures chosen for the bond are the cleric and one other party member (otherwise the question with the cleric being inside resilient sphere would be pointless).
Protective Bond states:
When a creature affected by your Emboldening Bond feature is about to take damage, a second bonded creature within 30 feet of the first can use its reaction to teleport to an unoccupied space within 5 feet of the first creature. The second creature then takes all the damage instead.
Force walls generally do not block teleportation (although there is a bit of uncertainty in some cases), and neither does resilient sphere. The isses are around targeting, and in case of protective bond there is no mention of targeting the space, so you will be able to teleport out. Note, these answers assume that the sphere does NOT move along with you when you teleport.
Resilient Sphere states:
The sphere is weightless and just large enough to contain the creature or object inside.
So, if you use the protective bond ability, you can teleport to an unoccupied space next to your ally. However, the space you are in (within your sphere) is not unoccupied, and the sphere is just large enough for you. That means you need to teleport into another space that is unoccupied, and that space will be outside the sphere, and you then will take damage as normal.
An interesting point is that resilient sphere also states:
A sphere of shimmering force encloses a creature (...)
So you can cast it on yourself, and it will enclose you. But there is nothing there that states it will do so for the entire duration. Whereas, if you cast it on an unwilling creature, the spell says:
An unwilling creature must make a Dexterity saving throw. On a failed save, the creature is enclosed for the duration.
One could argue that the highlighted text says that the sphere would move with an unwilling creature when it teleports, because if it wouldn't and the creature could teleport out, they would not be enclosed for the duration, which the clause demands. It only applies to unwilling creatures who failed their saving throw.
If your DM rules that the sphere will stick to teleporting unwilling creatures, you could then opt to resist the casting of sphere on yourself (although you could not willingly fail the saving throw), to enjoy the benefit of that ruling, and have the sphere travel with you as you teleport.
In that case, the sphere would protect you from taking the damage as
a creature or object inside can't be damaged by attacks or effects originating from outside
and the damaging effect originates from outside the sphere.
If your DM rules it works, the ability is limited to a number of uses equal to your proficiency bonus per day, does not work reliably (due to you needing to fail a save), and trying to set it up costs you a fourth level spell, all to negate one source of damage each time. I think that it would not cause a balance issue, but you may want to test this.