You didn't include your layout file, so I can't be specifically helpful, but in general terms, the outermost bounds across all of the elements in the view (or the bounds of the view itself) set the 'canvas', if you will. The elements are then placed based on their own bounds, and everything scales up or down to your screen, keeping aspect.
In your case, your backdrop defines the overall canvas, and you want to place your game screen in the center of that canvas.
Here's a test layout, discussed below:
<!-- test.lay -->
<mamelayout version="2">
<element name="myback">
<image file="mybackdrop.png" />
</element>
<view name="Simple 4 3 in 16 9">
<screen index="0">
<bounds left="2" top="0" right="14" bottom="9" />
</screen>
<backdrop element="myback">
<bounds left="0" top="0" right="16" bottom="9" />
</backdrop>
</view>
<view name="Simple 3 4 in 16 9">
<screen index="0">
<bounds left="18.5" top="0" right="45.5" bottom="36" />
</screen>
<backdrop element="myback">
<bounds left="0" top="0" right="64" bottom="36" />
</backdrop>
</view>
</mamelayout>
Centering a full-height 4:3 (horizontal) screen on a 16:9 backdrop is easy to figure out. 4:3 is the same as 12:9, 16 total width minus 12 game-screen width equals 4, half of that is 2, so you need to start 2 in from the left (2), and end two in from the right (14).
For 3:4 (vertical), you can try to figure it out by 9ths, but it's easier to convert both ratios to 36ths (27:36 and 64:36) then apply the same math as above. 64-27=37, 37/2=18.5, start 18.5 from the left, end 18.5 from the right (45.5)
As you can see, MAME only needs the proportions. You could use actual numbers of pixels if that would make it easier, as would be the case if you had a picture of an arcade machine open in a paint program and could measure distances between elements, but it's all the same to MAME.