The useful test is not difficulty. It is what happens when it goes wrong, and how expensive the fix is.
Genuinely worth doing yourself
Demolition. Physically hard, requires no skill, and it is a meaningful share of the labour hours. Removing tile, the vanity, the toilet and the old tub yourself saves real money.
Two cautions: shut the water off properly first, and on any house built before 1978, assume lead paint and follow lead-safe practices — or leave that part to someone certified.
Painting, at the end, when the room is otherwise finished.
Buying and staging materials, so nothing waits.
Accessories and hardware at the very end.
Cleanup and disposal, which is billable time if someone else does it.
Worth doing yourself with care
Vanity installation, if it is a straightforward set-and-connect.
Toilet installation, which is genuinely simple and where the only real risk is the wax ring and the flange height.
Tiling, if you have done it before or the room is small and the layout is simple. A first attempt at large-format tile in a visible shower is not the place to learn.
Leave to a professional
Waterproofing. The consequence of a mistake is a leak into the structure that appears years later, and the fix is removing everything above it. There is no visible feedback that it was done correctly.
Plumbing rough-in. Drain fall, venting and the valve depth all have to be right and all are inspected.
Electrical. GFCI, circuits, and an inspection.
Anything structural.
Anything that gets covered. That is the general form of the rule: work you can see and correct is a candidate; work that disappears behind tile is not.
Where DIY costs more than it saves
Doing part of a job and calling someone in to finish it. Contractors charge more to complete someone else's work than to do it from scratch, because they inherit the liability without having controlled the start.
Holding up the schedule. A trade booked for Tuesday who finds the demolition unfinished bills for the visit.
A mistake that has to be undone. Removing badly laid tile costs more than laying it correctly.
The middle path
The arrangement that works well is a contractor for the rough-in, the waterproofing and the tile, with the homeowner doing demolition before and paint and fittings after.
That captures most of the available saving without touching anything consequential, and it is a normal arrangement that most contractors will accommodate if it is agreed at the outset.
Say it upfront
A contractor pricing a job where the homeowner will do the demolition needs to know before quoting, and needs a date by which it will be finished.
Deciding partway through to take work back in-house disrupts the schedule and rarely saves what it appears to.
Tools you will buy and use once
A bathroom needs a tile saw, a mixing paddle, notched trowels, a level long enough to be useful, and a set of nippers. Hiring the saw is usually cheaper than buying one for a single small room.
Factor that into any saving calculation. Several hundred dollars of tools against a labour saving of a similar order changes the arithmetic, particularly on a small bathroom.
Time, honestly
A professional tiler lays a small bathroom in two days. A capable homeowner doing it for the first time takes considerably longer, and the room is out of service throughout.
Where it is the only bathroom, that time is the real cost of doing it yourself, and it is worth pricing against the labour saved before committing.
Insurance and warranty
Work you perform yourself is not covered by anyone's warranty, and a future insurance claim arising from it may be contested. That matters most for exactly the items on the professional list — waterproofing, plumbing and electrical — and it is another reason the boundary sits where it does.