When you bisect a ruler that measures 1 foot, you divide it into two equal segments. Since 1 foot is equivalent to 12 inches, you can find the length of each segment after bisection by dividing the total length by 2.
\[ \frac{12 \text{ inches}}{2} = 6 \text{ inches} \]
Thus, each segment of the bisected ruler measures 6 inches.