Okay, I see the problem. Your purse is made with Stockinette and Seed stitches. If you read the pattern carefully you can see the part where you are confused calls for stockinette stitch which is easy to increase evenly across the row.
Okay, make that purse!
Lois
Cast on 35 sts. Beginning with a p row, work in St st (k on RS, p on WS) for 9 rows (for casing). Increase 12 sts evenly across next row - 47 sts. Place markers on each side edge. Work in Seed st for 11 in. (28 cm). Place markers on each side edge. Work in Seed st for 6 in. (15 cm) more. Place markers on each side edge. Continue in Seed st for 11 in. (28 cm), end with a WS row. Place markers on each side edge. K 1 row, decreasing 12 sts evenly across row. Continue in St st, beginning with a p row, for 9 rows (for casing). Bind off