To find the number of bikini styles at Alec's Swimwear, we can calculate 19% of the total number of swimsuit styles, which is 100.
First, convert 19% to a decimal:
\[ 19% = \frac{19}{100} = 0.19 \]
Next, multiply this decimal by the total number of swimsuit styles:
\[ 0.19 \times 100 = 19 \]
Therefore, the number of bikini styles is \( \boxed{19} \).