Hi, It's Chris Watson from Ray White Ferntree Gully. Bayswater as a whole is going through a big change- It used to have a bad name for crime etc however now it is changing to appeal to young professionals. With the upgrades to the train line and ease of access to the city more and more young professionals are buying in the area.
Below is the link to an article that The Age wrote on Bayswater earlier this year.
Depending on which type of property you are wanting to buy I would suggest walking distance to the train station. The west side of Scoresby Rd typically commands a higher sale price but my opinion if that it is a nicer area.
Hope that answers your question. If I can help any further give me a call anytime on 0406 003 856.