After im done my workout, it takes around 20-30 mins to get home, should i bring a waterbottle and put some whey in it for after my workout, or should i just ride it out to have my ussualy shake of whey, oat, milk, and a banana?
take a bottle with you bro and have the shake in it for when you finish 
Also you may like to try WMS (waxy maize strach) its a fast acting carb source, or you can just have a gatoraide as alot of people do.
But like I said for your main question yes dude take your protein with you in a bottle to the gym.
How long is your workout? How well do you know the people at your gym?
Personally, I go to my gym and toss my drink to a friend of mine who puts it in their staff refrigerator. I used to use a mixed shake, but when I started doing that, I started buying Rapid Recovery in a premade bottle so I wouldn’t be too intrusive on their space.
Just try to work with the people around you… you’ll be surprised how helpful the people around you can be if you just ask.
For my post workout shake I do whey, gatorade powder and cream of wheat. If you use vanilla whey it actually doesn’t taste too bad and you don’t need a blender.
You can always take the banana and eat it there too.
Either way, the sooner you get your nutrition the better.
The sooner you can get that food in you after your workout, the better! Your insulin sensitivity is dropping every minute you don’t eat after working out.
Bring the shake with you, but make sure you are getting a solid meal in you when you get home. Pasta, meat and veggies are your best friends right after working out.