You have several solutions. The more realistic one would be to use a cloth simulation then use it as a Mesh Deform to deform your net. You have 2 much more simpler solutions, with Lattice and, more flexible, Warp modifiers:
Cloth: It's the most realistic solution.
- Create a plane about as large as your net. Give it a Physics > Cloth simulation, enable its Cloth Collision option. Pin it on its border.
- Create a ball, give it a Physics > Collision simulation.
- Animate the ball and simulate the movement of it hurting the net and falling on the ground. The net should deform accordingly.
- In the Properties panel > Object > Display, change the display of the plane, choose Wire.
- Bring your net object, give it a Surface Deform modifier, put it above the other modifiers. Choose the plane as Object. Click on the Bind button. Now the plane should deform the net.
Lattice:
- Create a lattice and in Object mode, scale it so that it encompass your net object. Subdivide it a bit.
- Give your net object a Lattice modifier. Choose the lattice as Object.
- Assign a vertex group to the whole net vertices except the borders that are supposed to be pinned, choose this group in the Lattice modifier.
- Put the necessary modifiers below the Lattice one.
- Select your lattice, in the Properties panel > Data > Shape Keys, create a basis shape key and add another one, keep this second one selected.
- In Edit mode, deform the lattice so that it deform the net the way you want.
- Back in Object mode, play with the value under the shape keys list. You'll be able to create keyframes to animate.
Warp:: This method is more flexible as it allows you to animate more easily.
- Create 2 empties, in front and behind your net.
- Give your net object a Warp modifier. Choose the 2 empties as objects From and To.
- If a part of the net is supposed to be pinned, select the vertex group in the modifier.
- In Falloff Type, choose the kind of deformation you want, you might prefer Curve to create your own one.
- You can move the empties, therefore animate the movement of the bump.