No such thing as a "working holiday" in Bermuda. Unless you mean getting sponsored to work here and thinking of it as a "holiday".
You cannot work here AT ALL unless an employer has
1. advertised the job in Bermuda,
2. no locals have applied, and
3. the employer is then willing to apply for a Work Permit for you.
There are NO exceptions to this rule. Nobody will hire you for anything without a Work Permit, because they can get into horrendous legal trouble, and it is not worth it.
After the above criteria are met, a Work Permit can take as long as 6 weeks to be approved.
Bermuda is a spectacular place to visit on holiday, and it is a spectacular place to work.
You just can't combine the two. Sorry if this is bad news!