I have done a lot of cycling and stopped a few months back, any exercise (such as squats, lunges etc.) just give me huge thighs and what I do not understand is, everyone else seems to look really nice and toned in that area, I feel like I just bulge out and makes me look way too curvy. I'm a normal size (size 6 upper, size 8 and 5ft 3).
I study exercise physiology at a university in florida. The answer to your question comes down to the physiology and nature of not just the muscle, but caloric accumulation. In order to achieve those"slimmer legs" you must not only tone the muscle, but burn the fat surrounding the muscles. Tracking your diet is important if you want to manipulate the visuality of any body part. The muscle will usually grow and "bulge out" as you say if you are eating more calories than you burn. The nature of the muscle in this situation is to "get bigger" and maybe even put on more fat if that caloric excess is significant. On the other hand. If you are burning more calories than you eat, then the nature of the body part is to burn and utilize fat as an energy source. Also, in addition to exercising, you are simultaneously giving definition to the muscle itself.
So the reality is...the girls that you see in the gym may have different eating habits than you do or maybe they are just genetically predisposed. But you should never compare yourself to anyone else. Instead start to understand the science behind it all.
Also, more aerobic workouts will help decrease muscle size, so I advise going back into cycling or any other endurance activity. Imagine a kenyan marathon runner and compare them with the body structure of an olympic weightlifter. The kenyan of course is much more slimmer in the legs, even the whole body. Why, you may ask? Because when the body is engaged in long durative events, it needs to preserve as much energy as possible, therefore there is an adaptation in muscle to decrease cross-sectional area which will help expend less energy per unit of time. This is an adaptive survival mechanism suited for that particular species lifestyle. How many times do you see those with bodybuilder physiques on a bicycle or running marathons? Its not a matter of whether they hate endurance activity or not, but how their exercise lifestyle has influenced the composition of their body. You dont have to worry about becoming too skinny though, since marathon running is not your occupation. Well, I hope I gave you a general sense of the direction you should be taking in order to achieve your goal and good luck! If you are persistent, you should see significant results starting on the 3rd week of your journey. Once you reach a satisfied composition of the lower body, then just adjust your caloric intake equal to your caloric expenditure to maintain that visuality.
I have a coworker who is a cyclist, and she complains about fitting in normal jeans because of muscle volume.
In such a case, there's not much you can do but stop cycling so much, and switch to other forms of exercise like running. There will be some atrophy.
If your thighs are fat, then you just have to burn the fat either through diet or exercise. This issue comes up quite a bit, but I highly doubt you could gain so much muscle that your thighs end up being bigger than they were when they were "fat". If you end up doing weight training, then keep your reps above 12 per set to avoid muscle growth.