For anyone interested, here is the final version. It's my first Wolfram Language function, so I'm sure it can be improved.

bee[] := Module[ {letters, z, k},

  letters = InputString[];

  z = Alternatives @@ Characters[letters];

  k = StringTake[letters, 1];

  Select[WordList[],     StringMatchQ[#, z ..] && StringContainsQ[#, k] && 

 StringLength[#] > 3 &]

    ]

Here is what the output looks like if the input string is fetbind:

In:= bee[]

Out = {"beef", "befit", "benefit", "biff", "defend", "define", "defined", \ "definite", "deft", "diffident", "edified", "effendi", "effete", \ "feed", "feint", "fend", "fete", "fetid", "fief", "fiend", "fife", \ "fifteen", "find", "fine", "finite", "fitted", "identified", \ "indefinite", "infinite", "tiff"}

The expression

"w" | "d" | "l" | "e" | "a" | "n" | "o"

is shorthand for

Alternatives["w", "d", "l", "e", "a", "n", "o"]

Here is a way to get there:

input = "wdleano";
chars = Characters[input];(* {"w", "d", "l", "e", "a", "n", "o"} *)
pattern = Alternatives @@ chars;(* "w" | "d" | "l" | "e" | "a" | "n" | "o" *)

But at this point I didn't understand how you wanted to apply this, because this pattern will match individual characters, but not longer words. So, I'd need more context to help with the next step.