Can I use a HC-05 and a GPS without a breadboard on a Arduino Uno?
I don't see why not. The breadboard is just something to help you prototype yuproect, in the end, your project should always be on a perfboard or a custom PCB.

Note that some male-female header might get handy.

I'm not sure that the HC05 can handle 5V though. You migh want to check.