In message , Cat
writes

How do you get rid of ground elder's network of tough roots to be able
to plant spring flowering bulbs in a bed?

At this time of year you don't. Their roots aren't very tough either.
The main problem is they are brittle and every bit that breaks off will
be a new plant.

Can I use soemthing like
Roundup, and will it get rid of the roots? Must it be applied while
the ground elder has all its leaves (I rather zealously zipped them
all, so if it does, I will have to wait till they show up again...)

Roundup will weaken it. But it is useless at this time of year. Plants
have stopped growing so using weedkiller will be a waste of time and
money.

The fastest way to eradicate ground elder is to hit it with glyphosate
when the first tender leaves appear in spring wait a couple of weeks and
then dig out the weakened plants. Also to hit it again and again with
any other broadleaf weedkiller whenever you happen to be using it.

You could do it all chemically or Organic(TM) style by sieving the soil.
But a combined approach is more efficient. Small bits of root affected
by glyphosate that get missed do not easily regrow.

How long after a Roundup application can I plant the spring bulbs, and
how long more do I have to plant them in time to get flowers next
spring?

Provided they haven't sprouted you can plant them immediately.
Roundup has to hit the plant to take effect.

A bit demanding, I am... But an answer would be truly appreciated!

You will have to dig the stuff out to be in time for this years bulb
planting.

Regards,
--
Martin Brown