To have a buckskin, you need a few things. First, a base color of bay. That means that the horse has at least one dominant gene for black pigment, E. Then you need at least one dominant gene for agouti, A, which restricts the black pigments to the points of the horse. Finally, you need one cream dilute gene, Ccr.
So your mare has at least the genetic makeup described above. She is at least heterozygous for A and E. She is definitely heterozygous for cream-- if she were homozygous for cream, she would be a perlino.
Now, if your mare is homozygous for black EE, and homozygous for agouti, AA, and you breed her to a bay or black or chestnut stallion, she will pass along an A and an E 100% of the time, so all of her offpsring will be A- E-, meaning bay based. Odds are that she will pass on her cream gene 50% of the time. So if she is AAEE you have a 50/50 chance of getting either bay or buckskin when bred to several different colors of stallions.
If you breed an AAEE buckin mare to a palomino, buckskin, or smokey black stallion (in otherwords, a stallion who also is heterozygous for cream) you still have a 50/50 chance for buckskin-- but now you also have a 25% chance of a perlino, and a 25% chance for bay.
If you breed an AAEE buckskin mare to a perlino or cremello (they are homozygous for cream-- called "double dilutes") all foals will have at least one cream gene since the homozygous-for-cream sire will pass one along 100% of the time-- you would get a 50/50 chance at either buckskin or perlino. No bay.
If your mare is Aa, your odds for buckskin decrease, as bred to an aa or another Aa horse their is potential for black or smokey black, rather than bay or buckskin. (or smokey cream, if the sire also has a cream gene.)
If your mare is Ee, your odds for buckskin can decrease, as bred to an ee or another Ee horse there is potential for chestnut or palomino, rather than bay buckskin. (or cremello, if the sire also has a cream gene.)
So if you are breeding to get buckskin, your choices will depend on a few things-- first, is your mare homozygous or heterozygous for AA and EE? If she is heter for either or both, you would look for a stallion who is homo for whichever or both.
Secondly, do you like or dislike double dilutes? If you do not want one, avoid stallions who have the cream gene. Breeding to stallion with the cream gene does not increase your odds of getting bucksin-- it DOES allow for getting a double dilute, thus decreasing your odds of getting a non-cream. So that choice depends on whether you would rather get a non-dilute, or a double dilute, if you do not get the desired single dilute gene it takes to get buckskin.