Hossain, 18, took three wickets on the final morning as the students were bowled out for 238 on Thursday.
Although Bangladesh had a first innings lead of 143, they opted for batting practice rather than trying to force a win.
Bangladesh captain Habibul Bashar made 75 and Shariar Nafees 50 before the game ended when the tourists declared on 246 for four.
Earlier, British Universities lost their last five wickets for 22 runs.
After Mashrafe bin Mortaza ended a stand of 134 between Luke Parker (65) and Josh Knappett (73), when Parker was caught behind, Shahadat took centre stage.
His second ball of the day had Knappett top-edging a hook to Javed Omar at fine leg.
Shahadat then bowled Amit Suman middle-stump for nought and also had Monty Panesar out for a duck, caught behind.
"It is healthy not to have preconceived conclusions on these guys and what Shahadat has shown here is that he really wants to play (against England)," Bangladesh coach Dav Whatmore told BBC Sport.
"I had only seen video footage of him playing for the A team before, but what he has done might mean he has leapfrogged everyone," he added.
First innings centurion Omar and Nafis Iqbal both fell to left-arm spinner Panesar when Bangladesh batted again before Bashar and Nafees spent time in the middle. They added 80, against a modest attack, before Nafess was run out.
Bangladesh have two three-day games against Sussex and Northamptonshire before the first Test of their two-match series against England starts at Lord's on May 26.
Brief scores: Bangladesh 381 (Javed Omar 167, Mohammad Ashraful 102) and 246-4 decl (Habibul Bashar 75, Shahriar Nafees 50) v British Universities 238 (J. Knappett 73, L. Parker 65; Shahadat Hossain 4-33)
Result: Match drawn