To patch a BPS file, you can use this website:

https://hack64.net/tools/patcher.php

Furthermore you can find information on this thread:

https://hack64.net/Thread-Web-based-ROM-patcher-APS-BPS-IPS-MOD-Star-Rod-PPF-UPS-VCDiff-xdelta

To apply the patch, first use the original Super Mario 64 (USA) ROM in the "ROM" section. Next, apply the BPS file in the "Patch" section for the ROM hack you want. You can then choose the file name below. To patch and download you ROM hack to your computer, click the "Patch" button on the bottom right. Once it has downloaded it is ready to be loaded and played.