When I was a graduate student at Stanford (in Operations Research, which is closely related to math and CS), the other students in the same program had gotten their bachelor’s degree at a very wide range of universities, nearly all of which were ranked about the same or slightly lower than UCLA. Quite a few but not all of the students in the same program had some relevant work experience after getting their bachelor’s before applying to graduate school. In my case I think that the work experience that I had plus the references associated with this was a big part of what got me accepted to Stanford.
GPA and research experience will be important. References will also be important. Whether or not you will need to get a master’s degree first will be difficult for me to predict.
I think that you are at a very good university that will give you great opportunities. You need to do your best to take advantage of those opportunities.
The east coast universities such as Columbia and MIT and Harvard are very well aware of the quality of west coast schools such as UCLA, UCB, and Stanford. I do not see any problem here. Also, it is normal to do your graduate work at a different university than your undergrad. This should not be a problem also.
Good luck with this and best wishes.