OP what seems apparent is that you don't have a very good understanding of a Headteacher's job. Which is fine, most people don't, except that you are trying to suggest they aren't doing their job properly. Putting aside the issue of how the bullying allegations have/have not been dealt with since November (as none of us know the full picture), I can say that your apparent belief that Heads should be contactable to you during non-school time is odd.
I deliberately call it non-school time because this applies to any time children aren't in school (i.e. evenings, weekends, outside term time). There are many, many important things that Heads are doing at those times and which they can't do while pupils are in school, as that time is largely taken up with dealing with day-to-day concerns. Much of this other stuff is strategic, some is crisis-management. The vast majority of parents would not be aware of what the Head is doing at any time of year, so your assumption that she isn't working because she isn't talking to you about a discipline issue may be completely erroneous.
To cite one example of a primary Head in England's first few days of 'summer holiday': Sunday afternoon in school to welcome back pupils and staff who'd been on a residential (ended up staying over 3 hours because the bus was delayed and then one parent didn't arrive for ages and the Head stayed with the pupil while other staff went home); Monday unplanned meeting in school with a member of staff and chair of governors after teacher received inappropriate gift at end of term and it needed to be followed up; 2 days this week had scheduled site meetings over new build; plans made to meet with chair of gov & deputy at some point in next fortnight over an unexpected staffing issue which cropped up this week. This is only what I know the Head to have been doing because my OH is the chair of governors and therefore has also been involved in these specific events. There will be many other things she's also been busy doing about which I know nothing. Admittedly, this Head may well be a better Head than the one you're describing, but who knows? The school isn't rated outstanding and I'm sure it has its issues in terms of bullying, some parents feeling response times are too long etc (i.e. external indicators might suggest to some parents that the Head could be better), but I suspect the reason I think this Head is good is because I have a glimpse into just what she deals with and how much time and commitment it takes to do her job - including getting done all those things which the majority of people will never notice.
I really, really dislike the assumption (increasingly common in education and perhaps other sectors too), that if you don't know what a person is doing for all of their working hours then they must be sitting on their arses. Why is the default belief that a person is being lazy/incompetent, rather than that they are dealing with other things which have been prioritised?