I’m an older lifter with no delusions of real strength just trying to stay stronger through the inevitable decline. Trying a meet it’s not completely out of the realm of possibility in the near future just for fun. But for the most part I’m just Lifting for General Health. Do you think it’s beneficial for a guy like me to rotate specializing in bench and press? I believe your position is that you can’t push both at the same time and I believe that to be the case for me through my own experience. Does it matter that much if you emphasize one over the other? If you had to choose one would you choose the bench over the Press, especially if I might try a meet sometime in the future? Right now I just started a second run on the bridge 3.0 so the bench it is for a while still but just wondering what you thought about this issue.
A meet is always a possibility, right? 
No, but really-
Does it matter that much if you emphasize one over the other? For the general trainee, no. We program with them both in the same blocks, one in a block, and one is usually emphasized over the other (with placement in the training day, volume, and variations) If you want to work on one and then the other, you can do that. Or you can simply make one slightly less important. This option tends to allow you to see better progress overall in the lift that you choose to emphasize.
If you had to choose one would you choose the bench over the Press, especially if I might try a meet sometime in the future? Most definitely if you want to keep competition as a possibility.
Yes I am torn because I enjoy doing both Lifts, although I think my shoulders like the bench better. Do you think that with maintaining the bench as the main lift and the Press as a supplemental lift, that the Press 1rm could still be inched up slowly? I hope this subject and questions aren’t too tedious and I appreciate your responses
This somewhat depends on where you are in your training. If you’re relatively new to training, I would just keep training both. Worrying about prioritizing one over the other when you don’t have an immediate need for a meet that uses one is kind of premature. You can certainly continue to do both lifts since you enjoy them.
What kind of programming are you doing now? It’s certainly possible to include the press as a lower priority and still get some progress. Yet again, your training history will factor in as to how much you’ll see and how long it will take to see that progress.
I’ve been training fairly consistently while working around a beat up old body for the past two and a half years. I did the starting strength LP, you know the standard fare, trying to run it out too long and getting injured, followed by two runs of the bridge free version then hypertrophy one and one run of bridge 3.0 . Right now I’m on my second run through the bridge 3.0. I’ll probably keep prioritizing the bench I would love to do 250 by the end of the year. My last peak which I did before the first run of bridge 3.0 I did 225 at about a 9. And of course Bridge 3.0 prioritises the bench so that decides it for now, at least until I finish with that, which I’m only in the second week of the second run. I appreciate your thoughts thank you for responding.