Did you make a separate class file for the test class or did you try to put it in the same file as the trigger? If the latter try moving it to it's own test class.

In terms of the test class itself, you have a good portion of it there, the only problem is you're assuming data exists on the org (so if you were to deploy the test class to a different org it would fail). Nor are you assigning the Home_Owner__c value.

So I would do something like this:

@isTest(SeeAllData=false)
private class UpdateOwnerRecordBulk {
    
    static testMethod void verifyOnwerIDChange() {
        
        Account a = new Account(Name='My Test Account');
        insert a;
        
        Contact c = new Contact(LastName='Test Contact', FirstName='Test', AccountId=a.Id);
        insert c;
        
        User u = [ select Username, FirstName, LastName, Email, Alias, Department, MobilePhone, Title, TimeZoneSidKey, LocaleSidKey, LanguageLocaleKey, EmailEncodingKey, ProfileId, UserRoleId FROM User WHERE Id = :UserInfo.getUserId() ];
        //Clone but get rid of the Id
        u = u.clone(false);        
        u.Username = 'testuser1111@testuser.com';
        u.IsActive = true;
        u.ContactID = c.Id;
        
        //Inserting the test user
        System.runAs(u)
        {
            // Perform our data preparation.        
            List<Financial__c> payments = new List<Financial__c>{};
            
            for(Integer i = 0; i < 200; i++)
            {            
                Financial__c a = new Financial__c(Home_Owner__c = c.Id);                
                payments.add(a);                
            }
                                    
            // Start the test, this changes governor limit context to             
            // that of trigger rather than test.             
            test.startTest();            
            // Insert the Account records that cause the trigger to execute.            
            insert payments; 
            // Stop the test, this changes limit context back to test from trigger.            
            test.stopTest();
                        
            // Query the database for the newly inserted records.            
            List<Financial__c> insertedPayments = [SELECT ID, OwnerID             
                                                    FROM Financial__c            
                                                    WHERE Id IN :Payments];
            
            // Assert that the Description fields contains the proper value now.
            for(Financial__c a : insertedPayments)
            {                
                System.assertEquals(u.Id, insertedPayments.OwnerId);            
            }
        }                        
    }
}

 This may still fail if some required fields are missing for the insert of records... but it should get you in the right direction.

Thanks that definetly helped. Here is my test class so far. 

@isTest
private class UpdateOwnerRecordBulk {
 
static testMethod void verifyOnwerIDChange(){
 
Id rtID1= [SELECT Id from RecordType where Name='Properties'].Id;
Id rtID2= [SELECT Id from RecordType where Name='Resident'].Id;
 
Account a = new Account(Name='My Test Account', RecordTypeID=rtID1);
        insert a;
    
    Contact c = new Contact(LastName='Test Contact', FirstName='Test', AccountId=a.Id, RecordTypeID=rtID2);
        insert c;
       
     User u = [ select Username, FirstName, LastName, Email, Alias, Department, 
     MobilePhone, Title, TimeZoneSidKey, LocaleSidKey, LanguageLocaleKey, EmailEncodingKey, ProfileId, UserRoleId FROM User WHERE Id = :UserInfo.getUserId() ];
    
     //Clone but get rid of the Id
        u = u.clone(false);        
        u.Username = 'testuser1111@testuser.com';
        u.IsActive = true;
        u.ContactID = c.Id;
        
    //Inserting the test user
        System.runAs(u)
        {
            // Perform our data preparation.        
            List<Financial__c> payments = new List<Financial__c>{};
            
            for(Integer i = 0; i < 200; i++)
            {            
                Financial__c p = new Financial__c(Home_Owner__c = c.Id);                
                payments.add(p);                
            }
                                    
            // Start the test, this changes governor limit context to             
            // that of trigger rather than test.             
            test.startTest();            
            // Insert the Account records that cause the trigger to execute.            
            insert payments; 
            // Stop the test, this changes limit context back to test from trigger.            
            test.stopTest();
                        
            // Query the database for the newly inserted records.            
            List<Financial__c> insertedPayments = [SELECT ID, OwnerID             
                                                    FROM Financial__c            
                                                    WHERE Id IN :Payments];
            
            /*
            for(Financial__c p :insertedPayments)
            {                
                insertedPayments.OwnerId = u.Id;            
            }
            */
        }                        
    }
}

 Error I am getting is on line 43 and the debug log says 

FIELD_INTEGRITY_EXCEPTION, only portal users can be associated to a contact: []

which makes sense since the contact user is not a portal user. So how do we enable the contact as the portal user in the code? 

Thanks so much for your help so far!

Reading this article and it looks like it could help http://wiki.developerforce.com/page/Apex_Testing_with_RunAs