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We study the late-time evolution of the central regions of two Milky Way-like simulations of galaxies formed in a cosmological context, one hosting a fast bar and the other a slow one. We find that bar length, R_b, measurements fluctuate on a dynamical timescale by up to 100%, depending on the spiral structure strength and measurement threshold. The bar amplitude oscillates by about 15%, correlating with R_b. The Tremaine-Weinberg-method estimates of the bars' instantaneous pattern speeds show variations around the mean of up to ~20%, typically anti-correlating with the bar length and strength. Through power spectrum analyses, we establish that these bar pulsations, with a period in the range ~60-200 Myr, result from its interaction with multiple spiral modes, which are coupled with the bar. Because of the presence of odd spiral modes, the two bar halves typically do not connect at exactly the same time to a spiral arm, and their individual lengths can be significantly offset. We estimated that in about 50% of bar measurements in Milky Way-mass external galaxies, the bar lengths of SBab type galaxies are overestimated by ~15% and those of SBbc types by ~55%. Consequently, bars longer than their corotation radius reported in the literature, dubbed "ultra-fast bars", may simply correspond to the largest biases. Given that the Scutum-Centaurus arm is likely connected to the near half of the Milky Way bar, recent direct measurements may be overestimating its length by 1-1.5 kpc, while its present pattern speed may be 5-10 km/s/kpc smaller than its time-averaged value.