You can define your abbreviation on "bit", and then test if it is preceded by "\", if so, return the new text, or "bit" otherwise.
function! s:Expr(default, repl)
if getline('.')[col('.')-2]=='\'
return "\<bs>".a:repl
else
return a:default
endif
endfunction
:inoreab bit <c-r>=<sid>Expr('bit', 'foobar')<cr>
That's the kind of tricks I used in MapNoContext().
EDIT: see :h abbreviations for the reasons why what you asked can't be achieved directly.
EDIT2: It can be easily encapsulated this way:
function! s:DefIab(nore, ...)
let opt = ''
let i = 0
while i != len(a:000)
let arg = a:000[i]
if arg !~? '<buffer>\|<silent>'
break
endif
let opt .= ' '.arg
let i += 1
endwhile
if i+2 != len(a:000)
throw "Invalid number of arguments"
endif
let lhs = a:000[i]
let rhs = a:000[i+1]
exe 'i'.a:nore.'ab'.opt.' '.lhs.' <c-r>=<sid>Expr('.string(lhs).', '.string(rhs).')<cr>'
endfunction
command! -nargs=+ InoreabBSlash call s:DefIab('nore', <f-args>)
And used with a simple:
InoreabBSlash <buffer> locbit foobar
or
InoreabBSlash bit foobar