I think Eliza must have left Bath with Willoughby more or less immediately after she left her friends. Bath was not really large enough to disappear in, and it was more than likely that someone such as her guardian would have come in search of her. I wouldn't think Willoughby would want to hang around to face the music.

I don't think Willoughby was with Eliza for very long for two reasons:
As you say she must have got pregnant very quickly. Whether Willoughby realised she was pregnant or not, I just can't imagine that a man so focused on his own pleasure would stick around long in the face of the 'delights'of morning sickness.

Also, although Willoughby may have known Sophia for quite a while, (".. she has had her own way at last"), he must have devoted some time to courting her between leaving Bath with Eliza and showing up Devonshire in September. No matter that Sophia was not a beauty, there must have been some other suitors for her £50,000, and it wouldn't be sensible to leave such a wealthy heiress 'on ice' for too long.