Final answer:
The process known as conjugation involves the transfer of DNA between bacterial cells via a cytoplasmic bridge, facilitated by a conjugation pilus.
Step-by-step explanation:
The genetic recombination process that uses a cytoplasmic bridge between the donor and the recipient is called conjugation. In this process, DNA is transferred between cells after a conjugation pilus draws two cells closely enough to form this bridge. Specifically, an F plasmid, or fertility plasmid, can be transferred between bacterial cells through conjugation, allowing for the exchange of genetic material and promoting genetic diversity within bacterial populations. This mechanism is particularly notable for its role in the spread of antibiotic resistance genes among bacteria.