In general, gallbladder removal (cholecystectomy) should not affect your bowel habits. Very occasionally, some patients may have softer stools which may give rise to the sensation of urge to defecate.
Various studies have also found that to be true [1]. Some patients reported less constipation and slightly more frequent defecations but short term recordings show no consistent change in bowel function. Only very rarely, patients experience clinical diarrhoea.
1. Hearing SD, Thomas LA, Heaton KW, Hunt L. Effect of cholecystectomy on bowel function: a prospective, controlled study. Gut. 1999;45(6):889-894. doi:10.1136/gut.45.6.889