Covary out?

Hi all! Thanks in advance for the help!

I have three variables A, B, and C

A is an independent, two category variable
B is an independent, continuous variable
C is a dependent, continuous variable.

I want to check if there is a relationship between A and C (i.e., are there differences in C across the two groups of A.) However, I believe there is a strong relationship between A and B.

So can some one walk me though the ideas, steps, tests used to "co-vary out" B?

This is what I've done so far:
1) First, run a t-test (or ANOVA) to test the relationship of A and B. [This came out significant, indicating to me some kind of strong relationship.]

2) ... this is where I am stuck.

Can I stick all three variables in an ANCOVA?
Do I need to add the interaction term? What if the interaction term is significant?
What if I don't add the interaction term into the model, and B is no longer significant? Does that mean I should remove B and just run an ANOVA with A and C?

Thanks again! Have a great weekend