The technology to print organs from raw materials - the patient's own cells, scaffolding material, and so forth - is in its earliest stages. There is some hope that this field could help to extend healthy human life by offering on-demand replacements for failing and age-damaged tissue. To date a few soft tissues, blood vessel-like structures, and bone have been successfully printed. There have been some important advances in using the self-assembly properties of living cells to do some of the work instead of the printer. The first replacement printed organs are probably more than a decade out, but there is a great deal more that could be accomplished beyond that goal.
When looked at over the long term, a broad category of modern technology might have a life cycle in the region of five decades or so. It moves from first experimental designs to mature uses in a few fields to a comprehensive portfolio of sophisticated uses in many fields over this fifty year span, and then its use declines as a new and better technology emerges. Definitions and time frames can be argued either way, but fifty years is a good round number that matches up with the life span of a number of 20th century technologies.
What can we envisage for the fifty year anniversary of bioprinting, in 2060, give or take a few years? What are the outer limits of the possible and the plausible? One starting point is the known conflict between young tissue and age-damaged systems in the body. Cells take their cues from the environment, and in some cases the environment has become actively hostile. Consider, for example, the death of motor neurons in Parkinson's disease: replacement cells may buy only a little time before they succumb to the same environmental issue that killed their predecessors. Also, we might think of muscle tissue that declines because stem cell populations in the old are instructed by their environment to perform less maintenance.
There are many whole-body, multi-organ, or regional biochemical feedback and control loops in the body. There are types of age-related damage that involve the intracellular accumulation of biochemical junk - simply replacing cells doesn't get rid of that. If your only tool is bioprinting (which won't be the case, but let us think inside the box for a while here), then the solution to these problems starts to look like replacing more of the body at one time. How much of the body could be replaced at once? Based on what is known today, everything except for the brain.
So one might consider a future bioprinting scenario in which an old body is completely discarded, the brain removed and placed within a printing vat. This machine would be something like an enclosed person-sized nutrient bath surrounded by interconnected machinery, feeds, bioreactors, and thousands of small manipulator arms and hair-fine printer heads. All controlled by sophisticated software and observed by medical technicians. There the patient would remain under sedation for however many months it required to print and assemble all the components of a new body. This would require a vastly greater knowledge of nerve regrowth than exists today, given that the brain would have to be reconnected to this body, but most of the remaining issues seem to be mechanical ones: how to assemble a bioprinted body (do you print it all at once in situ, or in pieces which you then move into place and print around?), how and when to connect vascular systems, and so forth.
The one thing you're left with at the end of the day is that this would be an old brain in a young body. Many of metabolism's controlling systems involve the brain, and an old brain has an age-damaged vascular system, vulnerable to surges in blood pressure. You can probably think of other biological mismatches that might cause disaster for an old brain hooked up to a vigorous young body. But these are problems that can be solved.
That said, I don't think the scenario I've painted above is plausible. It's feasible, but I strongly suspect that other branches of medical technology will make it obsolete before it becomes practical. 2060 is a world and a half away: we're expecting to see transformative medical nanomachinery emerge into widespread use by the 2040s, for example. For my money, a much more likely state of rejuvenation technology for baseline human biology in 2060 is the Strategies for Engineered Negligible Senescence vision: an array of therapies (or nanorobotic implementations) that remove biochemical damage in situ. Vaccines or artificial immune cells to clean out the buildup of unwanted biochemicals, replacing mitochondrial DNA or the mitochondria themselves wholesale, targeted destruction of senescent cells, swapping in new stem cell populations to repair everything else, that sort of thing. This would be less a case of tearing down the house to build a new one and much more a case of ongoing, period renovation.