What are options for Bi-Directional Replication of SQL Azure Database This questions came from a developer friend who is working with SQL Azure Database. 

Scenario: There are two Azure DB servers, one in North America, USA region and another one in South East Asia region. One way replication has been setup for a read-only replica to enable a local client to get data faster. The issue is whenever the client has to write data to the database, they need to write to North America, which incurs large latency issue. As a solution, they want to setup bi-directional replication between two servers to keep them in sync and thus allowing a client to read and write from a server located in their region.

I'm more of SQL Developer than DBA, thus, I'm not familiar with different options that could be available for bi-direction in SQL Azure DB. I have told him about SQL Broker and how I saw it used for near real-time replication and with some effort it could be set up for bi-directional messages, though not sure if it can be implemented in SQL Azure DB.
There is currently no option within SQL Azure for bi-directional (merge) replication. You could alternatively look at Azure Sql Data Sync or SQL Server on an Azure VM.