What proof do evolutionists have that bacteria or viruses evolve?
Scientists deal with evidence not proof.
See this site, and of course the nylon eating bacteria, here, which constitutes excellent evidence for bacterial evolution. For viral evolution, see here. A specialist, which I am not, would give more comprehensive evidence. And perhaps you should not use the term
Evolutionist ( Biological ) have evidence of change within the bacteria and viruses. This evidence of change is extrapolated into the Neo Darwinian theory of a common ancestor of all living things. Also called descent with modification.
Through plasmids bacteria readily exchange the genes they already have. This endows them with a capacity for rapid change. .....
Unraveling DNA Kamenetskii 1997, This rapid change is evidence for evolution as defined as change. However as a rearranging of existing information it is not evidence for Darwinian evolution.
Recently ( while studying bacterial resistance to anti bodies ) scientists found that in each strain bacteria had dropped from its chromosomes a gene called katG, which codes for the production of two enzymes catalos and peroxidase .... Apparently the (bacteria) cells had paid a price to defend themselves from the drug. They had made an evolutionary trade-off, giving up part of their own adaptive equipment for the sake of survival (The Beak of the Finch Weiner 1994
These are example of good evidence of evolutionary change but do not provide evidence of the creation of new information or proof of Neo Darwinian evolution ( See previous excellent answer about the difference between evidence and proof)
I repeat the line from an earlier answer :(https://socratic.org/questions/what-proof-do-evolutionists-have-that-bacteria-or-viruses-evolve#330035) that there are just evidences gathered in favour of evolution of microbes.
Bacterial population evolve in presence of antibiotic substances and many drug resistant superbug s have already evolved. Please read the following links to know how a resistant bacteria could 'evolve' from existing bacterial population.
Now about evolution of virus: there are few glaring evidences. First example that I would select is virus of AIDS: HIV which evolved from simian immunodefficiency virus (SIV). For details please read: http://www.avert.org/professionals/history-hiv-aids/origin.
Another example could be evolution of swine origin influenza virus H1N1.http://www.nature.com/nature/journal/v459/n7250/full/nature08182.html