Invisigun Heroes is a partial information game. All players make decisions based on what they know or can predict about their opponents. The pace and flow of the game largely depends on how much information is flowing. Many actions provide information to not only opponents but also to players themselves.
Positional information comes in the form of disturbances. There are many different types of disturbances which provide different levels information to each player. These range from firing your gun, which provides your exact location for a short period to sound effects that change depending on the surface the hero is walking on.
Moving carefully and not bumping seems like the best strategy. However, this would not provide any information to the other player(s) which would probably prompt them to also not bump. Bumping to trick your opponent into firing and giving away their location is a good idea, as bumps don’t give away your exact location.
It is important to choose a strategy that strategically provides enough information to keep the information loop flowing. That is, you create a disturbance that your opponent will react to, that provides you with information on their location and so on.