Mominul Haque was on 64 while all-rounder Shakib Al Hasan was five not out when umpires Paul Reiffel and Marais Erasmus took the players off at 1830 (0530 GMT) due to bad light and abandoned play 15 minutes later.
The players had left the field before lunch and tea due to persistent rain and returned during the third session only to be forced off before the umpires even reached the middle.
They returned for a final time about an hour later but bad light ended play after a frustrating 40.2 overs.
New Zealand captain Kane Williamson had won the toss and asked the visitors to bat, though Tamim Iqbal (56) refused to be constrained by the bowler-friendly conditions, hitting five boundaries off Trent Boult's opening three-over spell.
The showers, powered along by gale-force northerly winds, forced an early lunch after 11.3 overs with the visitors on 39-1, having lost opener Imrul Kayes for one, caught by Boult at deep fine-leg after he hooked a Tim Southee bouncer.
The 27-year-old Tamim continued to attack when they resumed and brought up his 20th test half century from 48 balls and had scored 52 of Bangladesh's first 56 runs.
He then hit his 11th boundary but was struck in front by Boult off the next ball and while he was initially given not out, Williamson had the decision overturned on review.
Mahmudullah was the only other wicket to fall when he was caught in the final session by wicketkeeper BJ Watling for 26 off Neil Wagner, who was unlucky not to also have Shakib when the ball burst through Mitchell Santner's hands at square leg.
Bangladesh bowlers Taskin Ahmed and Subashis Roy were given their test debuts, with the 21-year-old Taskin expected to lead an inexperienced pace attack.
Medium-fast bowler Kamrul Islam Rabbi has played just two previous tests.
(Reporting by Greg Stutchbury; Editing by John O'Brien)
