Rose bush

Hi there

I bought this yellow rose about 4 years ago, I think it is called a bush rose, its like a long stem and then forms a ball.  The first year it flowered lovely, the following second and third year not so good.  So this spring, I have really looked after it by pruning properly and bonemealed and put a 6 month rose miracle gro feed in it, however this year there are loads of offshoots on the side, its never done this before.  My question is should I cut these off so it will form a ball at the top more or just let the offshoots flower. Please see pic attached so it seems clearer.

Does anyone know what rose it is?  Its yellow, standard small classic rose shape and I bought it just like that, and forgot to take note of what it is.

It will look lovely once you've got it back to a clean stem.  It'll appreciate a bit of manure pellets now and then through the growing season as they are heavy feeders

Pity you don't know the variety. There are hundreds of yellow roses so I can't even hazard a guess