This relies on three different under-defined things:
how does arcane bond work?
how does the arcane bloodline version of arcane bond work? and
what counts as a warpriest’s “spells known”?
We don’t have solid answers to any of these questions.
Arcane bond and spell slots
For the first question, arcane bond is completely silent on whether or not you need to use a spell slot to cast the spell it gives you. We have a Q&A on the subject, but the only answer to the actual question seems completely irrelevant so far as I can tell. However, the answer is probably that you don’t need the spell slot, because otherwise wizards (the ones who originally got the class feature) would run into a problem of not being able to spontaneously use a spell slot for some spell. If they were expected to do so, you’d think it would be spelled out, something about giving up a spell they have prepared in order to cast a spell of the same or lower level from their spellbook. It doesn’t say anything like that, so spell slots are probably not necessary.
Arcane bloodline and needing to be able to cast the spell
The second issue is this: the wizard arcane bond feature says that it can only be used for spells the wizard is capable of casting. The arcane bloodline makes no such statement—it just says you can cast a spell known, and a parenthetical here explicitly notes how this is unlike the wizard’s version.
However, the “unlike” clause references “any one spell in the wizard’s spellbook,” which is not the entirety of the limitation on the wizard’s spells—the wizard also mentions needing to be able to cast the spell in question (this is important because wizards can scribe spells into their spellbook without being able to cast them).
Does the fact that the parenthetical doesn’t mention an override to the need to cast the spell mean that the sorcerer must also obey it? Rules as written, the answer is certainly not—the arcane bloodline says you get to cast any spell known, period, and the parenthetical is merely clarification and emphasis. Nothing says it works “as the wizard ability except,” which is what you would need.
So RAW, the arcane bloodline doesn’t require that you be able to cast the spell—but that’s assuredly an oversight, something they didn’t bother to mention because sorcerers can’t know spells they are unable to cast.
Warpriest spells known
Finally, on the third question, we don’t have any details whatsoever. The D&D 3.5e glossary indicated that wizards treated all spells in their spellbooks as spells known—see this answer for some details on why that still pretty unclear—but Pathfinder doesn’t have that glossary entry at all, and in any event it doesn’t extend to divine spellcasters at all (in fact, the glossary defined a “known spell” as “a spell that an arcane spellcaster...” though this obviously conflicts with that system’s spontaneous divine class, the favored soul).1
Realistically, deciding that divine spellcasters lack “spells known” entirely is probably a bad idea, with a lot of potential problems caused. Deciding that they instead know their entire list is also dubious, especially when coupled with the lack of any concern about spell level here. But RAW, that is the more-likely answer.
The official rules, as written, would seem to lean towards allowing the combination, barring some unfavorable ruling on spells known for divine prepared spellcasters, which would have to be made pretty carefully since there may well be collateral damage from such a ruling.
Personally, I would probably try to encourage my player to just... not take arcane bond, to avoid this mess altogether. If they really have their heart set on it, I would definitely limit it to spells of levels they can actually cast, at a bare minimum. That would probably be enough of a limitation for me, but if I was concerned about it, what I would do is allow the warpriest to keep a “prayerbook,” equivalent to a wizard’s spellbook, for the spells that they are able to cast using arcane bond. I would let them put two spells in it per level for free (same as a wizard), and then allow them to scribe any cleric spell they have actually prepared into the book without needing an external source but paying the usual costs and taking the usual time. Then it’s at least as balanced as it was for the wizard (if anything, it still costs more because the wizard gets a lot more usage out of the spells in his spellbook, while the warpriest only gets them once per day, but I figure eliminating the need to hunt down copies of spells mitigates that a fair bit).
- Emphasis mine.