Most so-called paradoxes in relativity are based on an
inadvertent or deliberate obfuscation of the limits of the
theory, in particular the finding that there is no absolute
spatial reference, as there is in Newtonian mechanics.

There's an old fortune-cookie game that we play whenever we go
to a Chinese restaurant.  Read the fortune as written and it has
a certain meaning; now read it again and add the words, "in
bed."  The meaning is completely changed (and if you've had
enough wine it's hilarious.)

Special relativity is like that game.  The meaning changes
completely if you don't nail down the wording.  Some shorthand
rules for non-mathematical treatments:

First: You cannot say, any longer, that "the mass is (blank)" or
"the length is (blank)"  or any other observation merely
"is" just that way.  You must always append the phrase: "as
measured by an observer in the system (something)".

Second:  You cannot say, "the time is."  There is no absolute
time and there is no universal common start time.  Time is
very specifically and interval between the observation of two
events.  If you combine this with rule one, you get the
clumsy  although more accurate phrasing: "the time interval (as
measured by blah blah)  between event A (as measured by blah
blah) and event B (as measured by blah blah) "

Third: You are not allowed to use the word "simultaneous" in its
usual sense.  "Simultaneous" means specifically a time interval
measured to be zero.  So its really a special case of rule two.

Fourth:  In special relativity, relative motion is always in a
straight line and velocity is always constant during a time
interval.  This is the same as saying that during the
interval under consideration, neither of the oberservers can
have any way of telling by any experiment who is moving.  You
are allowed to make a time interval arbitrarily small -
measure constant velocities before and after and add them all up
and that's how we figure out the effect of a force - but you
then have to realize that you can't use symmetry arguments to
create paradoxes based on larger time intervals.  This is the
basis, and the solution, of the so-called Twin Paradox.

Fifth: In special relativity, mass always and everywhere very
specifically means inertial mass.  We are used to thinking of
"mass" as synonymous with "quantity of matter."  That's not so
here.  In sr, mass very specifically means the ratio of an
imposed force to an observed acceleration (with, of course, the
proviso of rule one added to the words 'force' and
'acceleration."

If nothing else, such wordy rules should give you an idea of why
we use math instead.  It's much easier and quicker to write
down.

As to the situation at hand:

Let's rephrase it according to the rules, first.  Two observers
A and B are separated by a large distance and both are in
identical spaceships.  According to observer B, observer A is
moving at a constant velocity near c along a straight line and
coming right at B.

When you say "black hole" I have to assume that you are asking
if there are effects observed by B as due to A that B might
attribute to A being a very dense point mass.

Neither observer A nor observer B will see gravity waves or
anything like them.  Energy emission by wave propagation always
and everywhere requires acceleration, whether it is of a mass or
of a charge.  It is true regardless of the density of A as well,
even if A really is a black hole.  No gravity waves.

Similarly, "potential energy" as Eric means it is an unfortunate
shorthand for "work that would be done if an unstable system
were allowed to become stable."  It is not an intrinsic
property of mass or charge - it's a consequence of a
particular geometrical arrangement.  That's another issue
entirely.

So what =do= these guys see?

Observer A, in reference frame A, will measure the mass of
his spaceship as m.  Oberserver B, in reference frame B, will
also measure the mass of his spaceship as the same thing;
namely, m.

Now observer B applies a small force (as measured by B) to ship
A at right angles to the line joining them.  He does this in
order to measure the mass of A and finds that, as measured by
B, the mass of ship A is greater by a factor of sqrt(1-v^2/c^2)

Reset everything so everybody is on a straight line again.

Observer B again applies a small force (as measured by B) to
ship A but this time along the line joining them.  This time B
measures the mass of A as increased by a different factor;
namely [sqrt(1-v^2/c^2)]^3.

Reset everything so everybody is on a straight line again.

so far, we've found that the mass of A as measured by B depends
on the direction of the force applied in order to measure the
mass.  Black holes don't do that.

>From the point of view of B, does light bend coming around A?

I don't think so.  Lets put a star stationary relative to B,
well behind A and some distance off the axis.  A and B both will
measure light from this star as travelling at exactly the speed
c. A will observe red-shifting due to relative velocity; B
won't.  B will see no lensing around A since gravitational
lensing depends on the quantity of matter, that is on the
gravitational mass - not the relativistic inertial mass.

Some poppular books state the pinciple of equivalence for
general relativity as "there's no difference between
gravitational and inertial mass."  That's not quite right and
the distinction is the heart of your confusion.  It should be
"there's no difference between gravitational mass and intertial
rest mass."  (rest mass is shorthand for 'inertial mass as
measured by an observer with zero velocity relative to the
mass" in keeping with rule one.)

And if you want to get picky, neither phrase is really the
principle of equivalence itself, they are consequences of the
principle.  The actual statement is "for a given observer, there
is no way to distinguish between gravitational attrraction and
motion at constant acceleration"