Not a problem at all

Many people travel with luggage on the bus, though the bus can get totally packed and the scene at TXL to catch the bus can be a bit of a zoo. With one suitcase you should be fine. Note that Alexanderplatz is the bus terminus, so when you return to the airport you'll be first to board :) But I noticed that at some times of day when the traffic got heavy they would turn the buses early, around Brandenburg Gate, in order to keep on schedule. In that case you need to take the local bus from Alexanderplatz over there to catch the TXL. This doesn't happen often but it's worth noting; there is a lot of construction on that part of the route and it sometimes causes delays.

There is a ticket machine outside at TXL where you catch the bus. It's a fine way to get into town, in my experience.

Unfortunately I believe this is no longer the case. The last stop for the TXL bus is now just past Berlin Hauptbahnhof, and the bus no longer runs to Alexanderplatz.

From the BVG bus schedule (PDF, in German):
Ab. 4. August 2019:
Linienverkürzung. Die Linie wird vom S+U Alexanderplatz zum S+U Hauptbahnhof (bzw. zur Haltestelle Robert-Koch-Platz) zurückgezogen. Den entfallenen Linienabschnitt übernimmt die Linie 245.

From 4 August 2019:
Line shortening. The [TXL] line will be withdrawn from S+U Alexanderplatz to S+U Hauptbahnhof (or to the stop Robert-Koch-Platz). The canceled line section is taken over by line 245.

It's subtle, but the BVG network map has also been updated to show the truncation of the line.

In which case, is it quicker/easier now to get U/S-bahn? If I'm hopping off and on buses anyway? It won't be a heavy suitcase.

If I understand you correctly, yes I think so -- the fastest route is probably TXL bus to Hauptbahnhof, then the S-Bahn to Alexanderplatz. I can't imagine the 245 bus is going to be faster than the S-Bahn between the two stops in normal circumstances.

Why not take the X9 to Zoo.Garten and then a train (of which there are several options including S and U)?

That's what I'm looking at right now, as it happens. Last time I was in Berlin, I stayed near Nollendorfplatz, but as I wanted to pick up my race number from Tempelhof, I got the U-Bahn from Jungfernheide to Platz de Luftbruecke.

This time, because I'm arriving early, my priority is to get to Alex to drop my bag off, then to tootle around Berlin in the afternoon to my heart's content.

Looking at an U-Bahn map, it looks like the X9 follows the route of the U7 part of the way from Jakob-Kaiser-Platz to Wilmersdorferstrasse. Would it not be as quick for me to go that way to Charlottenburg and then S-Bahn to Alex?

I don't mind a bus, to be fair, but I have a greater sense of making progress on a train.

Yes but you have an extra transfer. I'd prefer fewer transfers as in Berlin they tend to involve lots of walking. Unless you know exactly where to board a train and/or you have timed a route to perfection. (c.f. the Green Park thread on the UK forum - I used to do the walk every day even though the escalator route is easier, but only because it saved a longer walk at another station.)

Ouch, that's too bad, it was so convenient. But maybe not surprising given the construction delays and the shortening of the route from time to time to stick to schedule. Good find, thanks!

Thanks for this. I know Green Park station quite well and can relate to the walking distances involved. Is that par for the course in Berlin?

I've found a route Bus-S-Bahn-Tram which drops me almost completely outside my hotel. I'm going to look at timings, as it'll save walking, perhaps. It's a shame the TXL doesn't go to Alex now, though, as this onward travel from Hbf si muddying the water a little.

Unlike in London it will all be covered by the same fare so if the tram drops you outside your hotel go for that. Not sure how walking distances at interchanges compares, I just remember having to go up and down lots of stairs and getting lost at the bigger stations (Alexanderplatz is one of the culprits).

Regarding the TXL bus, all I can say is that the first time I visited Berlin I nearly missed a flight when I took it on its full route, instead of taking a train and then the X9, as I was misinformed about the distances and traffic involved.

Thanks ever so much for all the help so far. You've been a fantastic hive of information. I might have some more questions yet.

Does anyone use the BVG app to buy tickets? I've got a phone for which I'm confident the battery will last all day, and I'd rather fire up an app and have a ticket ready to go than to hunt around for change for a machine.

Don't want to buy a 4 day pass as I have free transport on the Sunday with my race number.

I don't use app tickets unless they sell a ticket I can't buy elsewhere - but the app has been recommended in this thread. (E-tickets which are not tied to a single device are a different matter.)

No need for change, the machines take €5 and €10 notes and they should also take card.