Start windows 7 home basic.
Click on Start > Control Panel > Administrative Tools > Computer Management
Double click on Storage > Disk Management(Local)
Find the partition that Win7 Ultimate is installed(like D: for example)
Right click on it, select Delete Volume.
At this time you can extend your Win7 Basic partition to include the space that win7 ultimate had.
Right click on the Win7 home partition and click on extend volume.
It should show a max extend space to include the space that the Win7 ultimate volume had.
Click on OK to extend the volume to whatever amount of disk space you want(default should be the maximum space that is now available)
Let it work. It will take a few minutes.
Now to remove the boot menu item.
Go back to control panel.
Click on System > Advanced System Properties > Advanced Tab > Startup and Recovery.
Now that you only have one Windows 7 uncheck "Time to display List of Operating systems" and Select Windows 7 home basic in the drop down menu just above the box you just unchecked.
Select OK and restart your system to make sure it works.
Have a great day =D