interesting moment yesterday on final

So I went for a lovely flight yesterday, from Bedford (KBED) down to
Nantucket (KACK) for dinner. We flew down there in the last hour or so
of daylight with a smooth ride and great views, and then returned at
night with an even smoother ride and great night-time views, including
a few circles over Harvard, MIT and Back Bay on the way home. ATC were
very accommodating since it was fairly late.

Bedford tower was closed so I was on the CTAF frequency as I
approached the field. I was initially thinking of taking runway 24
since the winds were 190. When I announced my imminent arrival in the
vicinity of the field an aircraft informed me they were on final for
11. They also mentioned an aircraft in the area that was at 5,000 and
on an IFR flight plan but not talking to ATC, possibly inbound for
landing as well.

Armed with this information, I changed my plan and entered a downwind
leg for 11 (since the winds were not strong and that seemed to be the
established pattern). I announced my downwind leg, my base and my
final (looking out for traffic all the way). When I was at 1 mile
final, I hear

"Nxxxx, 3 mile final for 11, Bedford"
I respond with "I am 1 mile final for 11, Bedford"
He responds with "We'll slow it down"
This doesn't comfort me that much, since I'm only going 65 knots.
Maybe I should have said this to him at the time.
Then he comes in again with "We're going to break off our approach, do
a 360 and rejoin"
As I'm at 50ft, he says "Have you landed yet"
I reply with "Just about to touch down"

Then I land, clear the runway, inform him I am clear, and then he
lands. Everything works out fine although my landing isn't exactly a
greaser.

I didn't feel that great about the incident: did I do something wrong?
Why didn't I see him on final before I turned final (I specifically
remember looking in that direction before turning final)? What if the
timings had been slightly different?

And for his part, shouldn't he have been on the frequency and known I
was in the pattern? Shouldn't his first call have been a lot sooner
than 3 mile final? Shouldn't he have flown a circuit rather than come
straight in? I'm assuming he wasn't in any kind of emergency situation
as he would have asked me to go around.

Thoughts appreciated, especially from those with extensive flying
experience.

Tom