Not exactly, I said it would travel away from you at 10m/s until it runs out of energy i.e. the ball will accelerate away from you then decelerate until it's relative velocity is zero. There is an internal force between you and the bowling ball but after the event has taken place both you and the ball will be stationary relative to the earth and to each other (albeit further apart). The only thing that can disrupt this system is a force external!
This is not the case.
If we are in space, outside of LEO, frictional forces are minimal. If you are holding a heavy bowling ball that is 1/10th your mass and you push it away from you, you will accelerate in the opposite direction at 1/10 the rate. This is not a violation of any of Newton's Laws. His 3rd Law loosely states: for every action, there is an equal and opposite reaction. Most people get confused on this one because they think the action/reaction forces happen on the same object, but they don't. The Action here is you pushing on bowling ball with a Force. The Reaction is the bowling ball pushing on you with an equal sized force. Your acceleration and the bowling ball acceleration are not equal because you have 10x the mass, 10x the inertia. This also conserves momentum. If it is in space, the bowling ball when then keep its velocity, never speeding up or slowing down or turning until on 'outside' force acted on it.
In your example, if the astronaut and bowling ball were drifting away from Earth at 60 m/s, after the push, the Astronaut may be only going now at 58.4 m/s and the bowling ball may be going at 71 m/s (remember, they have different masses, so different accelerations), but the center of the mass of the system continues to move at 60 m/s. You are correct in stating that the we can't accelerate the system without an outside force, the Center of Mass does continue to move at 60m/s away from Earth, un-accelerated). However, parts of that system just need to follow newton's laws, and they do.
You may be confused in the thinking the astronaut immediately would have a velocity back towards Earth of pushing the bowling ball, but that simply wouldn't happen.
That's how rockets work in space. The combustion of burning the fuel slams into the focused nozzle of the rocket. The nozzle pushes on the hot gas, putting a force on all that gas, directing it out the back of the rocket. The gas then returns the force but opposite direction on the rocket, accelerating the rocket forward.
I mean no offense, but you sound a little confused about how Newton's 3rd law works.
Here is a question to check your understanding: If a large dump truck and a small ford fiesta hit in a head-on collision, which vehicle has the greater impact force? *hint: It's both. or neither. Their impact forces are the same.
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