Depends on what kind it is etc.

They don't bloom very frequently, although various fargesias have been going through a bloom cycle locally. In general, flowering - if not an outright signal of the mother plant's demise - depletes the plant's reserves. Growth halts during flower/seed production and the plant weakens. Many times the plant will look like it is dead and gets ripped out. And it takes time to regenerate a bamboo that has flowered, if at all.

See the attached link from the American Bamboo Society.

Here is a link that might be useful: read this:

My Farghesia nitida's never came back.

Where I work, we have two bamboos in flower, Fargesia adpressa and Pleioblatus shibuyanus 'Tsuboi'. I also had Fargesia n 'Nymphenburg' flower in my own garden. I have two small seedlings (I think) growing near where I used to have the mother plant. They might be small pieces of rhizome trying to grow, if they are, they are not trying to flower yet. I don't want to disturb them to find out.
I have heard of people saving a flowering Phyllostachys by chunking/cutting through the rhizomes in large maybe three foot squares, leaving the plant in the ground and then cutting off all of the flowers, a lot of work if you have a large grove but it may work. Some Phyllostachys aureosulcata bamboos will put up an occasional flower without hurting the plant but it does make you kind of nervous.

I have a hedge which started as two stems friends gave me about ten years ago. I'm not sure what it is, but probably some kind of Fargesia. I guess I'll cut it down and see if it comes back.

Have you checked to see if there are viable seeds in the flowers?

Yes, I would wait and look for seeds also rather than whacking it right down.

And if it is going to rejuvenate it will do that anyway. The idea that removing the flowering tops could assist or enable recovery would seem to only have a basis if the maturing flowers or seeds sent toxins down into the parts below, as occurs with some herbaceous plants (dead stalks are more stiff and better at holding up seed pods).