The 27-year-old Gilbert, who is thought to be Britain's only deaf professional rugby player, joined the Aviva Premiership club earlier this season from Scarlets.
Ex-Leicester back Hipkiss, meanwhile, has seen his season disrupted by injuries, but the 30-year-old remains a key part of Bath's plans.
"Mat is a special individual," Bath head coach Gary Gold said.
"He is unbelievably committed both to the team and to self-improvement. I feel proud to have him at Bath.
"And Danny is exactly the sort of professional we want around here. His work ethic is relentless and he takes no prisoners in training."
- Sports & Recreation