Question
Can I use Trifluralin 4EC herbicide to control grasses around new rose beds and existing roses. I have a real problem controlling weeds and grasses in gardens.

Answer
Trigluralin is a nasty one. The warnings are severe in regards to possible carcinogens and water toxicity
I would suggest RoundUp instead. This herbicide has been used in Europe for many years with no major problems, under the name of Murphys Tumbleweed. When sprayed on green matter this herbicide stops the plant from making a needed enzyme for a plant plant to grow. It works it's way down the plant's tissues and finally decomposes adding to the soil. The plant yellows, goes brown and then dies. RoundUp has no more plant killing activity past the soil line. So it is no threat to other nearby plants or their roots.
However for your use you can do it two ways.
One:- use a small black foam paint brush and stroke it on the weeds not touching the rose.
Two:- cover the nozzle of a spray bottle of RoundUp with a wax paper cylinder, toilet paper etc so you can guide the spray.
The liquid must come in contact with greenery to be effective and needs about 6 hours of no rain to do the job. Also not a wisdom to spray if there is any air movement.
If you are having mega problems with weeds and grass, is it possible to stop the problem at the source?  I understand your concern as I have 5 acres of hay and weeds next door to me. Hope this helps.