Yushien Garden to Matsue Castle direct way?

In Matsue I want to go to Yushien Garden and Matsue Castle.

I will arrive at Matsue Eki. I checked various sources in the internet, but there seem to be no direct connection between those two places? Must i really go Matsue Eki to Yushien Garden then back to Matsue Eki then again to Matsue Castle?

Would going by foot be an option? Distance seems quite far though...

Also a question: Can i use Pasmo to pay for the busses? I saw there is some kind of "water trip ticket" or so, but not sure if it is recommended to take this?

Thanks everyone!

Must i really go Matsue Eki to Yushien Garden then back to Matsue Eki then again to Matsue Castle?

The buses that connect Yushien Garden to Matsue Station continue on to Matsue Castle, so yes you have to go via the station but you don't need to transfer buses.

http://www.ichibata.co.jp/bus/rosen/shuttle-bus.html

Would going by foot be an option? Distance seems quite far though...

It's about 10km...