Burst in this case refers to the bursting or opening/ripping of seams or closures under certain kinds of stress.

THIS REFERENCE, from a US Govt document about protective clothing, DESCRIBES A BURST STRENGTH TEST

6.29 Burst Strength Test
6.29.1 Application
6.29.2 This method shall apply to LERL-1, LERL-2, LERL-3 and LERL-4 nonwoven
garment and nonwoven hand protection element materials.
6.29.3 Samples shall be conditioned in accordance with the room temperature conditioning
protocol (see Section 6.2.1) prior to testing.
6.29.4 Specimens shall be tested in accordance with ASTM Standard D3787.
6.29.4.1 This test method shall apply to the nonwoven outermost layer of all garment and hand
protection element materials.
6.30 Seam/Closure Breaking Strength Test
6.30.1 Application
6.30.1.1 This method shall apply to LERL-1, LERL-2, LERL-3 and LERL-4 ensemble
elements.
6.30.1.2 Specimens shall be tested in accordance with ASTM Standard D1683 with the
following modifications:
(1) Samples shall be conditioned in accordance with the room temperature
conditioning protocol (see Section 6.2.1) prior to testing.
(2) All specimens shall be taken from garment samples.
(3) Specimens shall include each type of seam and each type of closure.
6.30.1.3 The procedure for Test Specimens from Manufactured Items, ASTM Standard D1683,
Section 7.4, shall be used for testing. Seam strength shall be determined.
http://ncjrs.gov/pdffiles1/nij/221916.pdf

--------------------------------------------------
Note added at 13 hrs (2011-02-19 16:32:56 GMT)
--------------------------------------------------

And as to your question, Does it mean the "exposure time" of the workers?
I believe that the Burst Strength Test is meant to simulate the different types of conditions that will be face by the workers/users under different types of conditions.
So in a sense the answer to your question is yes - yes in that the concern is the time that the person has to accomplish a task before the integrity of the seams or the closures is no longer guaranteed to be reliable.

--------------------------------------------------
Note added at 13 hrs (2011-02-19 16:39:25 GMT)
--------------------------------------------------

THIS DOCUMENT IS MORE FOCUSED ON THE POSSIBLE BURSTING OF THE FABRIC ITSELF. If you need to know more about the subject, this should be a useful reference.

Burst strength –
Mullen
(ASTM D 3786)
A specimen is clamped over an expandable
diaphragm. The diaphragm is expanded by
fluid pressure to the point of specimen rupture.
The difference between the total pressure
required to rupture the specimen and the
pressure required to inflate the diaphragm is
reported as the bursting strength.
Burst strength indicates how easily
a material can be ruptured when a
force is applied by a blunt object
normal to the material’s surface.
Mullen burst strength is reported in
pounds per square inch (psi) or
Pascals (Pa). A higher reported
burst strength indicates a stronger
material.
Burst strength –
Ball
(ASTM D3787)
A specimen is securely clamped without
tension between grooved, circular plates of the
ball burst attachment secured to the pulling
(movable) jaw for the constant-rate-of traverse
(CRT) testing machine. A force is exerted
against the specimen by a polished, hardened
steel ball that is attached to the pendulumactuating
(fixed) clamp of the machine, until
rupture occurs.
Burst strength indicates how easily
a material can be ruptured when a
force is applied by a blunt object
normal to the material’s surface.
Ball burst strength is reported in
pounds force (lbf) or Newtons (N).
A higher reported burst strength
indicates a stronger material.
http://www.nfpa.org/Assets/files/AboutTheCodes/1999/FAE-EMS_...