There is to my knowledge no good solution to this issue. For some reason the good folks at apple have conflated the top of screen menu with the dock, and if you get one on any screen, you also get the other. Without resorting to a third party app, there is no way to have menu bars in each screen but lock the dock to the bottom of a single screen. (I would be glad to be proven wrong here, but I've looked a bunch and not found a way)
If monitors are arranged 'stacked' then the dock will be at bottom of the bottom monitor. However, few of us arrange this way and those who do would most likely not be asking this question.
If monitors are side by side, you can move it ALL-THE-WAY to the left or right and it will stay there, but that is not as requested (or as many people desire) at the bottom of a single screen.
You can hide it, so it won't obscure stuff, but it will still move around whenever mouse is 'bottomed' on a screen for small period of time. This might be the 'best' solution, provided you like a hidden dock, as you can then easily access it on any screen, but it is not in the way or annoying you by being seen to 'jump around'. It is rather there when you want it, and hidden otherwise. (I strongly suspect anyone doing usability testing had things set this way and thought it was just great, and why would anyone want to see the dock all the time anyway... )
You can turn off the each monitor is own space stuff, but then you lose having the menu bar at the top of each screen. Obviously folks have different perspectives, but one thing I HATED about mac's multi-monitor support was having to move to an entirely different screen to access the top-screen menu for a program open on a different screen. This was something I really like about mavericks (multiple menu bars) but sadly it seems to come at the price of the annoying jumping dock
If don't want a hidden dock, and you want top menus bars on each screen, and dock fixed at the bottom, the best workaround appears to be to basically disable all the new mavericks stuff by disabling 'each screen is its own space' Then get a utility like "Second Bar" which while discontinued is still available, as a way to get a menu bar at the top of each screen. I used Second Bar a lot with mountain lion and found it to work well (although you need to have a second renamed copy of the app for each additional screen) I have not used it with Mavericks so cannot say how well it does or does not work.