First of all I do think it is a good translation of the original Hebrew.
For example the ESV has essentially the same translation:
Numbers 28:10 (ESV)
10 this is the burnt offering of every Sabbath, besides the regular burnt offering and its drink offering.
Having said that there are some aspects of the Hebrew that are worth noting. For example the pronoun בְּשַׁבַּתּוֹ which both the KJV and the ESV render as "every" is perhaps more literally "on its Sabbath."
Keil and Delietz explain the opening phrase this way:
“The burnt-offering of the Sabbath on its Sabbath,” i.e., as often as the Sabbath occurred, every Sabbath.
Carl Friedrich Keil and Franz Delitzsch, Commentary on the Old Testament, vol. 1 (Peabody, MA: Hendrickson, 1996), 803.
Since the phrase would probably confuse more than help in the more literal rendering I can totally see why the versions use "every" and mention the word Sabbath only once.
The Hebrew word עַל־עֹלַת rendered as "Beside" or "Besides" carries with the idea of in "addition to," and when we think of it that way beside or besides does work. What the passage is saying is there was to be a Sabbath burnt offering in addition to the burnt offerings and the drink offering that were to be offered on days other than the Sabbath. KJV conveys that idea by saying a continual burnt offering and ESV as a regular burnt offering. Keil and Delitzsch say it was a "daily" offering but that might be adding too much when the thrust of the word is to carry the idea of a continual action.
Finally the Hebrew word וְנִסְכָּֽהּ׃ could be rendered as libation but if that is used then too much explanation is needed because in English we think of libation in a very different way than it is being used here. It was an offering to the LORD and not a recreational drink which is how we normally think of libation