I'm currently in high school, but I was thinking if it was possible to take a Psychology bachelors degree in the UK and then going to Med School at US? After all the research I found that the steps taken to be a psychiatrist is longer in the UK than in the US. Although since bachelors degrees in the UK are only taken in three years, and it is 4 years in the US, I was thinking of taking the psychology degree in the UK first. Will US Med Schools accept UK universities bachelors degrees?
It's fantastic you're interested in psychiatry and psychology is a great foundation for psychiatric study. I can't speak to all of the ins-and-outs of applying to an American medical school as an international student, though I imagine it would be quite competitive. You'll also likely run into several issues: for example, 1) taking the appropriate prerequisites (can you squeeze in calculus, physics, organic chemistry, etc. into your psychology degree? Would it still only be 3 years?), 2) taking the MCAT (which is very different from the UKCAT or GAMSAT), and 3) funding--you're talking about ~£9,000/year with generous repayment options versus >£30,000/year of private loans. The best way to learn more is to contact schools you're interested in and ask specifically about international admissions.
I can see you're mindful about how long medical training takes. 4 years of residency in very tempting. But there's a huge drawback: it will be very difficult to practice in the UK ever again with an American license. You'd likely have to repeat a lot of training and sit the speciality exams.
On the other hand, in the UK, you'll have to do 2 years of foundation training and 6 years of speciality training. That sounds like a huge difference (4 years versus 8), but the European model of training is generally much more humane and pays very well (ask an American resident how much overtime he gets paid, and he'll laugh at you... and then he'll cry). This might be a better long-term plan depending on your goals and preferences.
A third option is to do medical school in the UK and then apply for residency in the US. You'll have to sit the American licensing exams (called the Step exams) and do some rotations in the US to gain experience and letters of recommendation, but psychiatry tends to be open to taking international medical graduates for their residency programs (and I reckon it would be less competitive than applying for medical school as an international student). There are tons of posts on SDN about this option.