Thanks Bob for your help!
Wanted to give an update to this. Hopefully it will help others in this situation.
I took Bob's advice and backed up my website. After that I applied the update by uploading via FileZilla. For files with the same name as it was uploading, I selected "overwrite."
When all was finished, I checked the website and noticed I wasn't able to get to it! I would just get a blank page. It was the same for both the homepage and for the bolt login. I checked and noticed that it did not overwrite the config.yml file, so that was good.
I went to my backup and swapped the new htaccess file that came with the upgrade package with the one from my backup. Only after swapping that one file is when everything seemed fine. I was able to get to the homepage and the Bolt login. I noticed bolt updated to 1.5.1 and Symfony updated to 2.4.2.
I checked and noticed there were changes in the htaccess file. Hopefully this won't be a problem for me staying with the one that came with Bolt 1.4.4. It's been two days now since the update and everything looks okay except for one thing (see next paragraph). I was also able to post new entries without seeing any problems.
The only problem that I did notice is when I uploaded a .jpg via Settings->Uploaded Files, the file was uploaded, but it added a ".file" to the end of it. So the file would be "filename.jpg.file". The image would not show up in the "Files on the stack" box at the Dashboard. I was able to kind-of resolve this by going into the website via FTP and manually removing the .file at the end. With this I was able to work with the .jpg, but it was still not showing up in the stack box. I went into the database and manually removed the ".file" from the Stack column at the bolt_users table. When I did this the stack box disappeared all together! I changed it back so I can see the stack box at the Dashboard.
