[X] Withdraw, seek cooperation with the Ministry and the ruling family, go down as a group.
I think it's debatable as to which will be better at bomb defusal: there's too many uncertain factors. The more capable Renshu's preparations, the more likely going it alone will fail, but going it alone does have a higher potential payout. But in terms of what happens in the worst-case scenario, I think it's fairly unambiguous.
There's no reasonable grounds for blaming her for negative outcomes here, because the general security of the city is not her responsibility, and she doesn't have the official authority to go full cowboy cop here. True, that's fine if she succeeds (success needs no excuses, etc), but that's not certain. Meanwhile, if she fails to do this solo, she will absolutely be held responsible for the failure, even if the bulk of it was due to the Ministry and the ruling family not following up on her provided information. If she's doing it all solo, she's also in substantially more personal danger.
If it clear that we would succeed on our own, I would absolutely vote for the other choice. But in terms of the larger goal? Ling Qi's reputation is the coin we're trading in to establish ties outside the Emerald Seas and turn those enemies into friends, and reputation is like money: you need it to earn it. The reputation damage we sustain here if we go it alone and fail could kill a lot more people than the incident today.