There's a hole in fast bit of trail I used to ride regularly on the downs in Guildford. Sounds like the same dimensions as yours. If you ride at a slowish pace you ride down and up. A bit quicker and you need to be more active pumping the front wheel in and out. Faster than that, you need to manual.
I've never been that great at manualling, but the skill needed to hold a manual over a good length of road or trail is way more than you need to get through a bit of a dip. Just think about lifting the front wheel up before the dip and putting it down on the other side. If you can do that, the back wheel will take care of itself. As long as you concentrate on keeping the front wheel in the air until it's past the dip, you'll be alright. The more confident you get, the more you'll get towards a proper manual, pumping the back wheel through the dip, rather than a kind of front-wheel-only jump.
Faster still and your back wheel might leave the ground before landing on the opposite upslope, but you'll be relatively light on the bike anyway due to the front wheel beng higher, so you can soak the impact with your knees while the front drops down where you want it to.
If that happens more often than not, you'll probably be alright to try bunny hopping the whole thing.
