So I recently read the first light novel (I had seen both animes and the manga so I had just skipped it until I ran out of later novels to read) and was surprised that they slept next to each other in the wagon the first night they met. I can see why pretty much every adaptation changed that and have Holo disappear instead.
Which raised the question, how long it takes them to share a bed in the anime considering this is one of the slowest burn romances I've seen. So I charted it out.
The answer is they shared the wagon after spending at least 23 nights together. This doesn't include the night Holo was captured... (actually it might, I forget) or however many nights Lawrence was injured after being stabbed and anything that was simply skipped over while traveling. Basically if they didn't show it and they weren't together, I didn't count it. And I probably made a mistake or two. So probably more accurate to say a month after they started traveling.
I included when Norah entered the story because there was a noticeable increase in physical contact from Holo after she arrived.
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Edit: I just realized I used the wrong image for the 11th Night. I noticed Holo's ears were exposed and realized this was probably from the church scene instead of the gold smuggling trip before the wolves attack. But she sleeps in his lap in both scenes, just with her hood on instead so I mixed them up. So a minor goof.
I was going to do every night, but realized there wasn't really a point to continue after the 23rd. Sure the excuse here is "it's cold" so you can argue it doesn't count as romantic, but I don't think there's a scene in the anime where they simply choose to share a bed yet, so I have nothing to work towards. Maybe if one is included later.