Your interpretation is exactly correct; it's a pretty easy metaphor. Let's go line-by-line:
And now it's time for one last bow
I'm reminded of Shakespeare, here:
All the world’s a stage,
And all the men and women merely players;
They have their exits and their entrances,
And one man in his time plays many parts
As You Like It Act II Scene VII
A tradition in stage theatre is that, once the performance is ended, the cast comes out on stage and bows to the audience. Since the Doctor's "performance" (i.e. his life) is ending, it's time for him to take his bow (i.e. die).
I'm also reminded of the last words of the composer Beethoven, who also used theatre as a metaphor for life, and the end of a theatrical performance as a metaphor for death:
Friends applaud, the Comedy is over.
Ludwig van Beethoven
This may also be a sly reference to Sherlock Holmes; the story "His Last Bow", published in 1917, is chronologically the last adventure of Sherlock Holmes' life1.
Like all your other selves
This line is self-explanatory; the Doctor has had many "selves", all of whom have had their "last bow."
In plainest possible English: all of the Doctor's past lives have died, so this one must as well.
Eleven's hour is over now
This is where the clock metaphor comes in. "Hour" is often used idiomatically to refer to an unspecified period of time; see finest hour. Here, "hour" is being used metaphorically to refer to the span of one's life, so our time is up when our "hour" is up; compare to the classic metaphor of the hourglass2.
"Eleven's hour is over" means that the hour hand is leaving the space of number 11; literally, "Eleven's time is running out."
It's perhaps worth noting at this point that it's fairly common in the fandom to refer to Doctors by their number; One through Twelve3.
With these two facts in mind, the meaning of the line becomes obvious: Doctor number Eleven is dying. In the context of the following line, we might also say that this line is saying "this phase of your life is over."
The clock is striking twelve's
Recall my thoughts on the clock metaphor in the previous section; having left the space of number eleven, the hour hand is entering the space of number twelve.
When we say a "clock is striking" an hour, we mean that hour has been reached. The idiom comes from striking clocks, which audibly call the hour; Big Ben4 is a famous example.
So Doctor number Twelve is on his way up. In the context of the previous line, a new phase of the Doctor's life is about to begin.
1 Though not the last one published
2 TVTropes link; all hope abandon etc.
3 Personally, I prefer referring to them by actor, but whatever
4 Yes, I know it's not actually called that