Sort of, you might not like this
Let's start at the top: can a Giant Frog swallow you? Well the Giant Frog's swallow ability says:
The frog makes one bite attack against a Small or smaller target it is grappling. If the attack hits, the target is swallowed, [...]
So assuming you are Small (Halfling, Gnome, Goblin, Kobold; no Tiny PC options currently available) and are already grappled (which assuming you are willing and have time isn't a problem) it can swallow you. Now comes the bummer: in addition to being blinded and restrained, you take 2d4 acid at start of the frog's turn. No save, no option, just an average 5 damage per round. If you, nor your companions kill the frog, you will die. Congratulations, you just made yourself food for your own animal companion.
Rules-as-written the frog has no option to regurgitate a swallowed creature, though a reasonable DM might let it. So you may be able to infiltrate a bullywug base through this method, assuming you have a way to sustain 50 acid damage per minute1 and the bullywug don't question a unknown giant frog knocking on their door.
Regarding any precedence for creature transport, the Monster Manual includes (page 35):
The [giant] frogs' ability to swallow creatures whole provides a bullywug hunting band an easy means of carrying prey back to their villages.
This notably doesn't include the word "alive". So while it does imply the frogs can regurgitate swallowed creatures (otherwise the bullywugs would go through quite a number of them), it doesn't mean the prey lives. As for any acid damage to the swallowed prey, it is quite possible acid stained meat is a delicacy among the bullywug, it certainly no worse than some of the real-world human ones.
1: Most likely immunity if you can somehow pick it up. Resistance will half the damage, but 25 dpm is also going to be very limiting on your time/survivability.