If you are running the motor into a stop, rather than a L.S. etc, then you would need a little more intelligence.
i.e. sense motor current etc.
Looks like an ideal for a small micro with bi directional PWM etc, but may be out of reach if no programming experience?
Max.

 

There is an alternative to a transistor H-bridge, which would be a low-power relay setup, tow relays, possibly interlocked, one to run it in each direction. and then a mechanical switch that switches one or the other on when it reaches an end. I think that I have seen motorized toys that had that function years ago. So really, there are ways to do it with no electronics at all.
I am guessing that the whole thing is battery powered and so low power consumption is a requirement. But if your plan is to use a 9 volt radio battery then you need a really small motor.
So we need to know more about the application, such as the motor size and how long it needs to operate, and possibly a description of what the thing actually does.

 

It really is a bit hard to help as we do not know the detail of your project.
Can you get away with a mechanical system something like a windscreen wiper?
A simple double pole double throw switch operated by hitting stops et each end may suffice.
Or, detect motor current on stall to signal change of direction.
You could use a Polyswitch with reverse diode at each end to protect the motor.
Arduino or similar sensing the end or position and driving an H bridge or relay......
Lots of options.
A 9V radio battery is quite unsuited for motor control. Use 6 x AA cells in stead. They will last a lot longer and be cheaper too.