Here is the battle between droids and Gungan army, where droids entered the shield generated by Gungan army:
How did the droids get through the Gungan shield?
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This is addressed in the film's official novelisation. The shield has been tuned in such a way that it won't prevent human-sized objects moving at low speed.
When the racks were fully extended, they began to lower and separate outward, filling the open space in front of the transports with thousands of droids.
Positioned at the forefront of their army, General Ceel and his Gungan commanders exchanged worried looks.
The Gungan shield wall was designed to deflect large, slow-moving objects of density and mass such as artillery vehicles and small, fast-moving objects generating extreme heat such as projectiles from weapons fire. But it would not deflect small, slow-moving droids—even massed together in such numbers as they were here. Jar Jar Binks began to wish he were somewhere else, thinking that as mighty as the Gungan army was, it was dwarfed by the metal machine that marched against it now.
Because it's a ray shield.
In Star Wars ray shields are designed to "deflect" photon lasers and/or blasters, but they do not deflect physical objects.
That's why when the droids stepped into the deflector shield, they went right through.
Particle shields on the other hand can deflect physical objects, like missiles. These are usually on large capital ships, and/or any installment that requires protection from missile fire.
This concept is better explained here.
Which does bring up a point. Like, why didn't the shield also include a particle shield? Simple, because their troops would've been unable to leave the shield and they would be completely useless.
Another point is, why didn't they just bomb the Gungans? Well most likely because bombing them would've had a bunch of political fallback that they didn't want to deal with on top of the fallback from attacking Naboo in the first place. Or it could be that Palpatine who was orchestrating the whole thing, wanted the Gungans to win.