Space launches, ballistic missiles and perpetual motion machines
Without magic gravity-negating bubble technology, launching something to space from Earth requires packing it into an aerodynamic shell and ensuring it can survive massive G-forces. Then the payload is hurled into space, expending considerable energy. With a magic bubble, after doing some vector calculations simply place the non-aerodynamic payload on a platform with the desired speed (almost certainly on the equator) and at the correct moment activate the bubble. The object will continue moving with the speed of that point (470 m/s for a point on the equator, even without any additional impetus) unaffected by gravity or atmosphere. At the selected time the object phases back into existence at the appropriate altitude above the atmosphere for the desired orbit and the rockets can start firing to achieve the orbit.
Note: Achieving an orbit is not the same as getting out of the atmosphere. An object needs to achieve a speed of about 3 km/s for a geostationary orbit, but once clear of the atmosphere this can be done with an efficient, sustained low-thrust engine rather than a less efficient high-thrust rocket. It may even be possible to achieve some orbits by turning the bubble on and off repeatedly to take advantage of gravity boosts when desired while effectively ignoring gravity when it is not desired.
Long range space travel can also take advantage of the magic bubble - for example, once a ship is on the desired vector for Mars, activate the bubble so there is no need to worry about micrometeor impacts, radiation or solar flares for the duration.
Bad news - undetectable, unstoppable ballistic missiles. Nuclear ICBMs become vastly more dangerous with a strike practically undetectable until it has happened. A nuclear warhead can be launched at very low speed from inside a building - preventing any satellite detection - then drop its bubble at high altitude to allow gravity to accelerate it towards its target. Once on course it can activate its bubble again to render it unstoppable and undetectable until it drops the bubble for the final time milliseconds before it detonates. The victim of the attack cannot even tell who launched the attack, so they do not know who to retaliate against. Hostile actors without nuclear capability can use the same technique to deploy conventional explosives with varying degrees of sophistication, down to a suicide car bomb that drives at modest speed (to avoid attention) towards its target building, creates its bubble just before reaching the perimeter fence and some seconds later reappears and detonates inside the lobby.
Finally, like any other invention that messes with the base code of the universe, this can be used to create a not just a perpetual motion machine but a never-ending power plant. Lob an object upwards at a modest speed - say 10 m/s - and turn on the bubble, allowing the object to continue upwards unaffected by gravity and air resistance to the desired height. When the bubble turns off, the resultant potential energy will be turned into kinetic energy that can be harvested for power generation.