Google tells us the TMS1000 is a complete computer on a chip, so there are NO physical external connections to the internal bus, if there is one. What voltages are you looking at. Is there a clock signal to time to bus signals? The "bus" has to be something particular to the game electronics.
You do not need that. Your TMS1000 is a snail compared to any Arduino. Lets assume you have taken care of the physical layer e.g., via level shifters. In your sketch you read the input signal, apply your transformation and then write the signal to the output pins. Rinse and repeat.
As Paul said, having a clock signal could help synchronize your sketch to the TMS1000.
Did you split the bus? You cannot just write to the same physical bus.
Oops lost large part of my message.
The Hornby Zero1 ;model train controller is what I am using. Which as it is works very well and the only thing I would like to improve the number of locomotive addresses over I can handle that. http://www.princeton.edu/~mae412/volume.html
has a lot of info and explanations and plus my attachments to earlier message.
The arduino would have a 16 keyboard and be used for entering numbers above 16 say #18 etc
So original keyboard on controller would be used up to #16 and output on the original bus, as designed. The Arduino keyboard will insert ? or whatever info into the pre-existing data base and then return the bus to the railroad tracks for disimination by the loco receiver.
Hope this helps. Apologies for missing this info in original email above.