Actually, applying to doctoral programs from a bachelors is the standard way to do it in the US. There isn't, normally, a lot of benefit of taking a masters first.
Most undergrad programs, with some exceptions, don't provide serious research experience, so it isn't normally expected. It is a plus if you have it. But the admission system is very broad based.
The first couple of years in a doctoral program are mostly advanced coursework leading to comprehensive exams. A separate masters may help you avoid that, or not, but it depends on a lot of factors. Better to stay in one program that is designed to get you to the point of doing the research that the doctorate requires.
Normally, comprehensives assure that you have a sufficiently deep knowledge of the general field that you don't necessarily get as an undergraduate. Hence, the advanced coursework.
Some doctoral programs start you out earlier with research so that you have the basic techniques down. Some will give you a masters along the way, perhaps just by asking, perhaps by writing a thesis.
One advantage of this path is that you have quite a lot of experience and contact with the faculty by the time you need to choose a research advisor for your dissertation. Having the right advisor is a big plus.
Some lab sciences are a bit different, but if they permit applications from undergraduates it is still the best course of action for most.