Recommend a small tube amp for bedroom use?

If you don't mind EL 84 tubes, the little Jolida 102B integrated is a great little amp with a very small footprint and at 19 watts per channel can drive a variety of small, inefficient if necessary, speakers. You won't need a preamp and can find them on Audiogon used for $300-$400. I am currently driving Spendor S 3/5s with one in a second system with great results.

Look at the Italian brand Synthesis. Very compact and nice looking. Nice sounding too, though not cheap. Also, it is pushpull (I recall one model used EL84s).

Sophia Baby?

I've got an Acoustic Masterpiece AM-201 integrated from AirTight with EL84 tubes. Small footprint, handsome. Sounds superb. 22w per channel, can drive 88db speakers easily. A link: http://www.axissaudio.com/amplifiers/ampAmast.htm

I am looking for a small and affordable 300B, but I don't currently have high-sensitivity speakers

Bedroom speakers won't need more than a watt or 2.

Take a look at a small SET like decware. I'm using a pair in my bedroom system now.