It seems like you are not sure if you should increase the weight on your bench press--but you can't get stronger if you do not increase the weight.
As mentioned previously in this thread, in order to increase the weight for the work sets on the bench press for 1-3 pounds every workout (if in novice phase) or weekly (if you are an intermediate), typically microplates are used, as noted in the article linked by Coach Rippetoe above and in the blue book (Starting Strength: Basic Barbell Training (3d ed.), p. 304).
See if you can keep making progress every workout with microplates. If that doesn't work, then consider switching to intermediate programming by trying a volume day and an intensity day. Here are some recent thoughts on that topic by Coach Delgadillo:
Intermediate Programming for the Upper Body Lifts | Nick Delgadillo
Press and Bench Press Programming - Getting and Staying Unstuck | Nick Delgadillo
Good luck!