No more than a blind person walks slower in game I would suppose. Normally when a new type of movement is gained but the speed isn't listed, its speed matches your base land speed
No more than a blind person walks slower in game I would suppose.
A blind person actually does move slower in the game; if you're blind, you must succeed on a DC 10 Acrobatics check to move faster than half your speed. If you fail, you fall prone.
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But as to the OP's question: Unfortunately, Paizo's rules say nothing at all about how burrow works. I'd say the intent isn't for an elementally wild-shaped druid to burrow blindly.
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As a minor oddity that may also boggle you...
Tremorsense lets you pinpoint "things" in contact with the ground (I'm sure I can remember reading though that standing still foiled it... Maybe 3.5 days).
There's nothing to say anything more than that. I don't think its mean you have any better sense of anything more than "something large and heavy is 35 feet away from you in that direction". You still can't "see" per say what it is and what might be between you and it or anything. Even with it, you can't see anything more than with it. Depending on your interp of 'Thing' is a 40 foot cube of unmoving iron ore that you cannot dig through able to be perceived with tremorsense (and are you able to perceive you can't burrow through it). If not, what happens if you move full tilt into it?
Compare and contrast to (say) blindsense which has the same-ish function but things don't need to be touching with the ground for blindsense to function.
Anyways.... RAW though... Unless there is something I missed, reduced speed your referring to is a function of the blinded condition, which you do not have. I'd say you can move at full speed, but without a sense of where anyone else is or where the ground 'ends' if your surfacing.