I was in same situations before

One time, the new company offered me a sign-on bonus to compensate my potential bonus.

The other time, the new company couldn't offer the sign-on bonus, but luckily I was able to negotiate a later start date (2 months after the offer date), so I didn't have to miss ~10K ESPP/RSU profit.

Not sure how much your bonus will be, for 2~3K, I'd say forget it.  For more than 5K, if you don't care to burn the bridge with the old company,take a vacation from 4/22~5/3, and give notice thru email once you receive the bonus. Take some days off from the new company in week 5/6 and go back to old company for job transfer and exit interview...

don't know your position, but make sure your company has no policy against you doing so...

2 weeks notice is always nice, but you have to do the best for you and your family.