I don't see how you could get around (and why you would want to get around) using one context per DB since using two databases also requires two connection strings.
You mention the table attribute, are you using code-first (the question is tagged with database-first)? In database-first approach you would just use the wizard to create an additional context, in code-first you would use something like this (along with DB1Connection / DB2Connection connection strings in your config):
public class DB1Entities: DbContext {
public DB1Entities() : base("DB1Connection") {
}
public DbSet<Table1> Table1 { get; set; }
public DbSet<Table2> Table2 { get; set; }
}
public class DB2Entities: DbContext {
public DB2Entities() : base("DB2Connection") {
}
public DbSet<Table3> Table3 { get; set; }
public DbSet<Table4> Table4 { get; set; }
}