Let's denote the number of flowers in each bunch as \( x \). Since Kari picked 23 bunches of flowers, the total number of flowers she initially had is:
\[ 23x \]
After giving away 46 flowers, she had 138 left. This can be expressed with the equation:
\[ 23x - 46 = 138 \]
To solve for \( x \), we first add 46 to both sides of the equation:
\[ 23x = 138 + 46 \]
\[ 23x = 184 \]
Next, we divide both sides by 23:
\[ x = \frac{184}{23} \]
Calculating the right side gives:
\[ x = 8 \]
Thus, the number of flowers in each bunch is \( \boxed{8} \).