Getting a Masters first gives you more background, which means you may start research a bit sooner in a PhD program. Also, if you are unsure of your interests, it would give you time to think about it so that you apply to appropriate PhD programs. (Maybe - if it's a one year Masters, you'd be applying for PhD programs after only 1-2 months in the Masters program.)
However, Masters programs in the US are not guaranteed funding. In some universities, the programs are really just a money making venture. Students from the US rarely have a Masters before going to a PhD, unless they feel unprepared for a PhD program and are trying to improve their application. I'm guessing from the way your post is phrased that you are international. If you want to get a Masters first, I would suggest applying somewhere with a 2 years research Masters rather than a 1 year course-based Masters. The 2 year one which involves a thesis is actual preparation for what you have to do in a PhD, and it's certainly beneficial to have the experience (although unclear if it's worth spending 2 years at it - this is a personal decision). These programs are more common in the UK, Europe, or Canada, and often offer funding. A 1 year Masters is basically more of the same from your Bachelors, except with somewhat more difficult courses (maybe - depending where you're from, the courses may actually be redundant and/or too easy for you).
In an American PhD, the first 1-2 years are typically spent taking courses, very similar to a US Masters. Indeed, you usually get a Masters degree along the way to the PhD, e.g. once you have passed qualifying exams or advanced to candidacy, you can get a Masters (specifics depend on the program).