You can start going around the outside of the ring as soon as the rider ahead of you does their final salute. I make sure I use the time to get my horse familiar with the ring/judges stand/decorations. Many rings are made of plastic boards and, when footing hits it it can make a loud noise. I ride as close to it as I can to let them hear this ahead of time. I cross between the judges stand and the ring, then make a wide turn and cross between them again. The stand is often WAY scary and the horse should see it with both eyes. THEN, I work on really getting the horse moving nicely and try to relax the whole situation.
Once the bell rings (or whatever signal your ring is using) you have 45 seconds to enter. That is a pretty long time. Don't hear the ring and turn so sharply that you squeal rubber to rush into the ring. This will get you AND your horse too tense. Make a nice large slow turn, swing nice and wide so that you have a straight entry into the ring. As soon as the bell rings, take several deep breaths and make yourself relax.
If you are at a show with several rings side by side, Make sure you know what signaling device YOUR ring is using. Each ring will have a different device. It is up to YOU to know what your ring is using. It is not uncommon for a rider to make a mistake and enter their ring on another rings bell. A bad way to get eliminated.
Have a great time and PLEASE post a video of your ride. I would love to see a western dressage ride!!