My employer is offering me financial incentives to stay, but I'm looking to move on. How do I respond?

(This is my first time posting here. I apologize if I'm missing certain information; I can provide more if needed, I was simply trying to not risk identifying myself.)

The leadership at my company has undergone some changes in the last few months. My team, including myself, are not entirely on board with some of their decisions and while we still have job security, the situation that our team is currently in is not ideal.

As a result, the 2 other members on my team have resigned and my boss has just given his resignation notice. I'm the last one left and the company desperately needs me to stay. Given my job role, they could fairly easily fill the position but they would be hurting quite a bit until that happens.

My boss's boss (who is soon to be my new boss) has just offered me a 10% salary increase along with a 10% bonus (based on the new salary). 50% of the bonus would be paid immediately, the other 50% in 6 months. However, if I resign within the next 12 months, I would owe the bonus back to the company. The dates coincide with a major project that our team is working on; essentially, they want me to stay until the completion of the project.

As I stated earlier, the situation is not ideal and I've been looking for other opportunities outside of the company. I've voiced my concerns to my new boss and I'm certain part of the reason that I'm being presented with this offer is because he's aware of how I feel and is worried that I may be looking for a new job.

I do have another job lined up and there's a very good chance that I would be extended an offer. This job is with a company that's in an extremely ideal situation, given my field, and I would be looking at approximately a 15% salary increase.

I feel like if I accept this offer that I would be expected to stay on for the next 12 months; and that if I don't, my new boss would be quite pissed, understandably. He's a good guy and I really don't want to burn any bridges. I'm leaning towards politely declining the offer but I don't want it to seem like I'm declining it because I'm actively pursuing other jobs.

How do I approach this? If I do decline the offer, how do I word my reasoning for doing so?

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