Is it a lump sum, or are there unit prices associated with all the other work items? If it's the latter, you can fix the other unit prices, and have a basis for negotiating the price for shoring, thereby getting what you need and, with luck, saving the owner some $. Their shoring price shouldn't be any higher than the other bidders' prices. If it's a lump sum, there are still ways, but you would need to have the right staff who could do independent cost estimates, and require the bidder to show the basis for estimating all the work items.
If the low bidder is presented with the issue before the contract is signed, he may withdraw his bid. If you were to accept the bid, THEN point out the problem, there might be some legal implications for you, and a small contractor could end up being driven into the ground before the project is done - can't get blood from a turnip - and everybody loses. Riggly above mentioned the issue of a 25-foot trench box being feasible. If you and the owners accept a proposal that you know is of doubtful feasibility, seems you are asking for huge claims, and maybe worse.
It's probably the owner's call, but you'll still need to cover your own butt in case the neighbor's footings are affected by the lack of shoring. If they aren't doing what you think is correct, send them a registered letter describing the risk and your recommendation not to proceed without real shoring. Don't know if that's complete protection for you, but it would help in getting their attention.