Black holes are three-dimensional in reality. If you were two-dimensional you can imagine to enter the black hole from all sides. From the left, from the right, from the front, from the back, and everything in between and at different angles.
The same holds for a 3d hole. You can imagine it to be builtt up from an infinity of the funnels in the black hole wire picture. All these funnels are connected with each other to form the 3d space structure. So you can imagine that you enter the hole from the left, from the right,or from the top (which isn't possible for a 2d hole.
The metric for a 2d hole is a 2d Schwarzschild metric with one angle missing.
So you can imagine a 3d black hole as a 3d funnel, consisting of an infinity of angular connected 2d funnels.
The accelerated motion is a natural state so to speak, without forcing a oarticle to change its motion. So if you involve time then a particle would follow the natural path of a geodesic. Inside the horizon all geodesics are inward directed.
This can be seen in the 2d funnel model. The path of all particles, even the ones whose velocity is an outward directed lightspeed, is ending up at the center (as you can see in the model there is not a real center point though as the funnel extends to infinity).
It might seem counterintuitive that an outward direct geodesic is not possible. It is easy enough to draw one. But remeber that also time is involved. If time were reversed all geodesics would be pointing outward! Like in a white hole.
So the 3d black hole can be approached frim all directions in 3d space just as a 2d hole can be approached from all directions in a 2d space.
A black hole can have two mouths though. There are various wormholes of which the Einstein-Rosen bridge is the most known:
More precisely it is a transcendental bijection of the spacetime continuum, an asymptotic projection of the Calabi–Yau manifold manifesting itself in Anti-de Sitter space.
There are more double mouth wormholes. They have in common that the black hole can be approached from two disconnected pieces of space. Though a white hole connected with a black hole cannot be approached from the white hole side where time goes backward and everything can only come out of the hole.