Barony Bridge is unique in the way that it has two park entrances, with a path leading straight from one entrance to the other. In the beginning you won't have many researched rides, nor are there any pre-built rides.
Start by building some thrill and gentle rides along the bridge. The Wooden Roller Coaster is very expensive, so you should consider concentrating your research on Roller Coasters in the beginning. Both the Bobsled Roller Coaster and the Steel Wild Mouse Roller Coaster will then be researched very soon. Just use the Water Slide as a substitute until then. Make sure to build rides close enough to the bridge so they attract the attention.
Roller coasters are best to be build away from the bridge to expand the theme park. Later in the game, you can connect the rides on both sides of the bridge via a transport ride (i.e. the Chairlift).
Notice that if you won't put research on stalls and rely only on Burger Bar and Hot Dog Stall, you will get the "Worst Food" park award, which will give your guests an excuse not to come to your park, so put research on shops and stalls too for a while in the scenario.