The officers of Moav who accompanied Bilam were surprised that such an important person was riding a donkey and not a horse. Bilam at first made excuses and said his horse was out in the pasture, but his donkey spoke and blurted out that in fact Bilam always kept it around because he was was committed bestiality with it (Sanhedrin 105b).
What kind of silly excuse is it to say the horse is in the pasture -- so go get it!
I heard in the name of the Pnei Menachem of Ger a bekiyus fact that answers this question. Chazal (Sota 11) tell us that Iyov, Bilam, and Yisro were all advisers to Pharoah. After Moshe warned of the plague of barad, the Torah relates that the servants of Pharoah who feared Hashem took their animals in, while those who did not pay heed and ignored Moshe left their animals out to be killed. Targum Yonasan explains that "HaYarei es dvar Hashem" who took his animals in refers specifically to Iyov, while "Asher lo sam libo el dvar Hashem" who left his animals out refers specifically to Bilam.
That's what Bilam meant when he said he left his horse out in the pasture -- he left it out in makkas barad and it got killed, while the donkey which he kept inside with him was spared.