Bulk MgB2 samples were synthesized by hot isostatic pressing under pressures up to 200MPa at 950 degrees C. In these conditions, full densification of samples was obtained (similar to 98% of theoretical density). SEM, EDS and XRD analysis on final dense bodies were used to evaluate samples, and show increasingly better control over the amounts of secondary MgO (down to similar to 10%) and complete prevention of formation of MgB4 by using simple glass encapsulation techniques and addition of Mg(s) to the capsule. The samples display superconducting properties, including a narrow critical transition in electrical properties (Tc similar to 36-38K). Magnetic studies were performed, allowing the determination of the superconducting fraction and critical current density J(c) of the materials. Contrary to the Tc, the J(c) is quite sensitive to the processing and microstructure and values from 0.3 to 0.6x10(6) A/cm(2) are obtained at 10K. The reduction of J(c) with the applied magnetic field requires further improvements to reduce weak links.