Cycling is one the last holdouts when it comes to strength training. Virtually every other sport embraced it years ago (decades for many) to improve performance and prevent injury. The thinking went that building muscle means adding weight, and adding weight is the enemy of cyclists, whose strength-to-weight ratio is paramount.
However, you can gain strength without adding significant muscle mass (hypertrophy). Powerlifters and wrestlers have to be strong, but need to stay in their weight class, so they avoid gaining extra bulk. One way is to lift more weight with fewer reps with more rest between sets. This recruits more muscle fibers and motor neurons, but doesn’t stimulate the excessive muscle growth that bodybuilders are looking for.
The benefits of strength training for cyclists includes increased muscle endurance, injury prevention - especially for older athletes as our bone density decreases, a stronger core, better bike handling skills - especially in mtb and cyclocross, and also just being a more well-rounded athlete.
The web has many resources for weight exercises for cyclists, or better yet, hire a strength coach to walk you through the routines and check your form. Form is paramount when lifting.
The article below is a great primer for the types of exercises you can start with. Virtually all can be done at home with a few dumbbells or kettlebells, and none of these will add bulk.