Having two Beddies of my own and being a groomer, the Bedlington trim takes some time to master. I'm still nowhere near mastering the "perfect trim" but I like to think my dogs don't look too bad lol.
I have messed up so many times on my two, our client Bedlingtons are all clipped off

so I only get to trim my own horrors lol.
Honestly loads of owners give it a trim, don't be scared to go for it. It's actually fun grooming your own pups.
I recommend getting a Bedlington Book, maybe you already have them as you have a Beddie lol. They usually show you a trim. I could try and copy you the pages from Notes from the Grooming Table - they show you the exact trim and I follow it a lot.
Generally you'll need Clippers, Scissors, matt breaker, comb, Blades. It's good to be shown how it's done. There may be videos on Youtube just to give you an idea.
I'm lucky as I use a lot of my equipment at work. I recommend going onto groomers to check equipment as they are generally pretty good price wise and the equipment is really good.
Here's some pictures of my first breed standard attempts on my pups.
I have to say Suki - wee black one, doesn't suit breed standard trim. She's off the working Beddies her shape just doesn't suit it. Bailey suits it far better...